First of all, I do want to say that it's pretty obvious that a lot fo work and revisions have gone into making FE. I don't know how most people feel, but customer service these days in most any industry is nonexistant. I feel this is pathetic and unforgivable, but it is what it is. For this simple reason I'm tickled that Stardock has chosen to take this on, to offer us a chance to play the beta and make suggestions to help them make this a better game, and in the end give the game to this group of folks. I know that many feel it is "owed" to them since EWOM was more-or-less a failure, but there is no law requiring them to do this. Yes--there is the thought of their reputation--but honestly, if they didn't make good on EWOM but made an awesome game years later, people would still buy it. After all, as I have said, no other company seems to care about customer service, so why should we even expect it? Now let me get off of my soapbox 
Here we go:
1) Champions. I'm not sold that the chamions are too powerful. There is nothing more fun than creating a guy who weilds enough power to decimate a small continent. If I want to be grounded and pick and poke at a task, I'll just go to work. However, I *do* think that the champions are unbalanced. When I walk into a battle as a lone adventurer, and my opponent is a hero for another faction with several units, I ought to most likely lose. Sure, I can destroy a lot of his units with a fireball, but he ought to be able to focus on me and crush me into oblivion. This doesn't happen. The enemy heroes don't seem to develop high-level magical skills, and if they do, they sure don't use them. I mentioned this in another post, but I *love* the system in Heroes of Might and Magic V. I have yet to have a hero that is better equipped than the AI heroes. All of their equipment buffs the troops in their army, and thus you can throw dozens of top-tier units to their death against lesser troops if the hero is good. This makes it neawrly impossible to steamroll everyone as each faction has some tough troops. When you do fight a major battle, you have to take most fo your troops to do it, and you lose most of them leaving you vulnerable to other factions. Essentially, the game isn't won until it is 100% won. It makes it a nailbiter to the very end.
In summary, keep the heroes as awesome as they are--just make other fation's heroes tougher and better able to resist your power. You'll STILL have that feeling of god-like-ness when you swat that group of spiders in one round that used to destroy your armies a few rounds back.
2) Champions. Don't let them just sit around. Lots of valid comments on this. It's too easy to kill "unclaimed" enemy heroes for great equipment. In fact, do like MoM and HOMM--have heroes come to you for hire. This would make the prestige really count for something. They won't come to you AT ALL below a certain level, and then just low-end heroes. As prestige climbs, so does the level of hero that approaches you, and better-equipped. Make prestige sought-after... keep leveling a very slow process so that you can get better heroes from high prestige than leveling them on your own. But definitely let the heroes *come to you*.
3) Mobs. Have roaming monster groups, sure, but have some really powerful ones also guarding critical areas such as nodes. This will keep the player-versus-environment part going for much longer. You'll have to work hard to make a foothold before you go out trying to focus on enemy factions (at present, why do the work? I cruise the map for all of the underdefended cities and let them do the work for me).
4) Magic. I absolutely DO NOT like ditching the spell research. AT ALL. That was one of my primary focuses in EWOM... and it worked. I did not like, however, how any hero at a certain level could cast any spell that you know. You could limit this by establishing spell learning for each hero. Here's one option that would be interesting:
Your faction can research spells, but it is sloooooow. Perhaps just have "research" with a slider to choose how many points go to tech and how many go to magic. Have scrolls with spells guarded by mobs, where upon defeating them this spell becomes available to your faction. Maybe even have some spellbooks with multiple spells (3 or 4) that are part of a tough quest. Thus, you either have to go through very intensive research to learn spells, or find them. Once found, each hero, if they do not know the spell, must learn them. Perhaps they have to remain idle for so many turns based on the spell to study and learn it. Or, they can learn it while adventuring, but it takes 3 times as long. Allow heroes slots per level on spells they can learn. Thus, a level 3 hero might be able to learn 2 level 1 spells and one level 2 spell. This would make having multiple heroes *matter*. Also, if a hero comes to you with a specific spell, you can "research" that spell 3 or 4 times quicker since he can teach it to your faction. Same with taking an enemy city... if they know a spell you didn't you can now research it faster.
5) Magic. I still think that spell damage should be linked to specific shards, such as you do more damage with fireball based on the number of fire shards you have. BUT... if you're in a game with no fire shards (or just one), or can't reach some, overall shards should still have an effect other than generating mana. Do this by area of effect and/or duration. For instance, fireball, when you control any one shard, will damage the target as well as the tile to the left and right. Control any 3 shards, and it affects the target as well as the front, back, left and right tiles. Control 5 shards and it affects a 3x3 area. You could even get really creative and say if you controlled 3 air shards, there was a 50% chance of the fireball creating a wind that knocks opponents prone for 1 round, Etc., etc. Stack it up to 15-20 shard control and it will make playing those large maps FUN.
6) Magic. What about fizzle? If you're a mage who just learned fireball, or your spell skill isn't so high? what about a chance for it to fizzle completely and/or perhaps work, but do a bit of damage to you (or other members of your army)? This will keep the mix of fighter/mage somewhat limited. Perhaps the more metal in your armor will cause spells to short circuit and/or backfire. Also, a mage carrying a two-handed magical sword? Come on. Make magical staffs with minimal melee damage but double, triple or even quaruple the caster's skill, making you prefer a staff over stronger melee weapons (and perhaps very powerful wands with absolutely no melee damage?).
7) Settling. I'm sorry, but this was terrible to implement. Every single piece of land out to be colonizable in the game. Maybe have some squares with 0 food/resource, but let me *choose* if I want to settle there to makes my area of influence contiguous. Also, PLEASE include "proposed" settling spots when I mouse over the "settle" option like in Civilization. Sometimes it's very hard to tell by just looking at the numbers.
8) Area of influence. It seems that monsters are less likely to come into these in FE, but allow that area to mean something. Allow me to have a setting (again--using the overall "resource" slider) to choose a general defense option for my area of influence. Based on this setting, monsters are more likely or less likely to come into the area. If they do, they take some set amount of damage per round until they leave the area. Or, if not a slider, allow me to sacrifice troops to a "guard fund" that sets this value. Basically, those troops are now patrolling my borders. The defense of these guards is based on their original defense, and grows as I build more forts, etc., but the damage they do depends on their original attack value. We have to have some way to guard our caravans and damage any enemies overall as they spend time in our areas (this would also keep enemy factions from trying to traverse your lands at any time, as well as keeping me from doing the same). Honestly, if an enemy faction I can squash asks me to leave their area but I need to get somewhere, I'll just say, "I want to see your head on a pole". It does no good. AND... if you're at war with a faction, make the damage taken within this area be doubled or tripled (since you'll be focusing on getting them out). If This would make you MUCH less likely to go to war, as it will really soften your troops otherwise and leave you vulnerable.
8.5) Are of Influence. Have a research item for "tower of supression" or something. Basically, anytime the enemy comes into your territory (or you into theirs), it hampers the effectiveness of your spells based on the research level and/or structures built. This is magnified during times of war. Easy way to implement this? You could have this be a function of shards you (or they) control. It might make it so influential that your first goal in a war is to take out their shards.
9) Cloud Walk, etc. For some reason this spell DOES NOT work for me. Thus, I'm not sure how it's implemented entirely, but I see people complaining. To keep this from being a game breaker, make it so you CAN NOT teleport into any area of influence (even your own). Thus, if an army is about to attack one of your cities and you're across the map, sure--you can teleport back close to that city, but not within the area of influence. Thus, you'll have a turn or two of walking to make it to your actual city (this will also boost the building of road networks since you can travel much faster on them). This will keep you from freely exploring the map leaving your cities unguarded, and also keeps you from teleporting right beside an enemy city and attacking it. Obviously, the bigger the city, the bigger the area of influence, and the further away you'll be when you teleport to its vicinity.
10) Roads. There ought to be research for roads. The more it is researched, the faster units can move on them (as well as caravans). Faster trade=more money, and faster movement for troops is always a great strategic ability (see #9). You can also implement a % chance of caravans being caught. The slower the caravan, the more likely it is to be destroyed. The faster, the chance lessens.
11) Big compliment here. I LOVE the casting delays on spells. This REALLY makes levels important. If you want to cast fireball immediately, you want to become impulsive (+10 initiative on first attack). Thus, you cast it and boom! It's ready to use. VERY good job here and great implmentation of one attribute boosting another. LOVE IT. Cast fireball again? You'll be waiting.
12) Mounts. I've only had warg and horses, but do any mounts do damage? If so, great! If not, they should. If I'm riding a spider, warg or whatever, one enemy (even at random) ought to take damage from my mount every turn. This makes horses the most basic since they won't do this. However, on ANY mount, you ought to have a "charge" option. You choose a single enemy within your range, choose to charge them, and it does triple damage to them but negates some degree of your armor rating during the charge. It has a one-turn delay (here again--impulsive would be great). Great for melee heroes and/or mounted troops. Also, maybe have a chance to be dismounted based on your level vs level of the enemy, leaving you prone for one turn. Mounted units should be more powerful, but if you enter into melee with those troops there ought to be a chance for you to lose your mount.
13) End Game. I agree that there needs to be an overall way to extinguish an enemy quickly that is mostly beaten. However, I *hate* razing cities and so-on. There needs to be an option for the enemy to surrender to you, allowing you to take over their cities. However, since this could seriously unbalance the game, give those cities a penalty such as a 20-round cooldown where they produce nothing for you, and you cannot control any building, troop production, etc. OR give them a 50% penalty in production since they're not happy about their new landlord. Or a PERMANENT 50-75% reduction in production until you station troops within the city to calm things down.
14) End Game. Perhaps have a "Pursuasion" Spell that is cast on a particular enemy. It costs a LOT of mana to cast, and for it to work you have to allot some specific amount of mana per season (say it costs 2000 mana to cast, and you can choose any amount per season--even more than your income--to boost it). Say you have 10,000 mana, you cast it, and you have 8000 mana left. If your income is 50 mana/season and you choose to boost it for 200 mana per season you can maintain it for (8000/150) 53 seasons. The enemy has to counter this spell with the equivalent amount of mana, and if so, there's no effect. But when (if) their mana runs out before yours, there's a % chance one of their cities will turn their allegience to you (based on city level). This will help "peacefully" tie things up for you. You have to choose a high mana/season to drain your enemy, but keep in mind that once you drain him you have to keep it going at that same cost to convert cities over to you. You can't cancel the spell and re-cast it with a lower number due to a cooldown period (maybe 50 turns on that faction), not to mention the initial cost of 2000 mana.
I'm going to wrap this up for now since it's gotten so long. I hope there's some stuff in there that looks pretty good, and I would love for some folks to make suggestions on some of the points I raised.
Again--thanks Stardock for sticking with the game. It's not perfect, but there's nothing else on the horizon that can offer what you *almost* have at this point. Keep up the good work!