I don't think you have explained what you are asking very well.

But reading between the lines as best I can, I can only say

"Dude - you are playing Sins with major end game fleets meeting. Expect to lose some ships"...

Right.

I'd swap the 40 Assailants for the equivalent worth of Enforcers or Transporters. Those things suffer against Advent Fighters, while HCs and Fighters wouldn't fare that badly.

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As for the strikecraft, here's a little comparison table I made ages ago:

Fighter Squadron:

Advent             9      40/1         378 HP     11.7 DPS Laser                       144s
Vasari              4      85/3         391 HP     10.4 DPS Phase Missile             96s
TEC                 6      60/1         378 HP       9.6 DPS Autocannon              120s

Bomber Squadron:

Advent             7        75/1         551 HP     17.5 DPS Beam                     126s
Vasari              3      140/5         525 HP     17.1 DPS Phase Missile            90s
TEC                 5      100/2         550 HP     16.5 DPS Missile                    125s

It shows ships-per-squad, hull/armor-per-ship, total squad HP, total squad DPS and total squad build time. Total squad HP factors in Armor as 5% Hull per point of Armor. This is also not including technology upgrades, which is in the advantage of Vasari and TEC since they have easier access and better armor/hull upgrade capabilities while strikecraft are not affected by Advent's superior shields. Vasari construction times are also a fair bit better and both their squads use the same weapon.

But all those advantages are hogwash because the Advent have got moarr squadrons!!! While 1 Vasari Fighter Squad may be capable of neutralizing 1 Advent Fighter Squad, the Advent have an extra squadron in each carrier and each hangar that can fly without being contested.

I don't know the cost of the Advent carrier, but it is more.  Also, the Advent carrier takes up 20 fleet supply, while the Vasari takes up 14.  So, if you think about it, the Advent had 55*1.5 carriers to your 50 carriers.  I should also note that Advent SC pop like flies, and the vasari do not.  I don't know why you had 30 subs, you don't need that many.  I also notice that you don't have any LFs.  LFs counter Carriers by destroying the ship.  Jam weapons also works for taking out the first wave of SC by allowing your SC to survive and do some damage.

Here's the main problem with your play philosophy, you are focusing on killing the SC without killing the ship that builds them.  You need the LFs to attack the carriers and destroy them.  Once the carriers are dead, it is just a matter of time before you get air supperiority.  LFs take only 50% damage from SC, and do (I think) 100% o 125% damage to Carriers.  LFs are also faster than carriers to they can chase them down.  Additionally, all LFs have some AM damage tech that you can research.  Carrier's produce SC with AM.  Without the AM, those carriers are nothing more than cannon fodder and cap ship food.

[EDIT] Advent hanger bays also cost more and take up 6 tactical slots as opposed to 4.  You can't even build an advent hanger bay on most worlds without upgrading your planet infrastructure first. 

I'll give that a shot. I never use LFs since HCs do twice the damage, have twice the HP, twice the shields, and more than twice the armor for less than twice the cost. You seem to know what you're talking about though.

Ill scuttle 10 subverters, 10 LRMs and 10 HCs to build 32 LF's

I suppose this means the primary role of heavy crusiers is to tank the damage, not dish it out, eh?

If I recall, the enemy DID have a Mothership and Raptuure. They fell before the power of the Egg in the beginning of the battle though.

Well, I once had around 20 Kodiaks, 2 Sovas (lvls 5 and 9), one Kol (lvl 7), one Marza (lvl 6), one Akkan (lvl 8) and one Dunov (lvl 5), 40 Percherons, 50+ Cobalts (Just a small boost for firepower and to add some bars to make my fleet look powerful lol), 10 Gardas, 2 Cielos, 20 Hoshikos, 15 LRM's. I lost at least around 270 Supply Points worth of units, including some of the following:

20 Percherons (IDK How, I think it was their Illums), 15 Kodiaks, 20 Cobalts, 3 Gardas, 5 LRM's, 1 Cielo, 15 Hoshikos, and I'm honest to god I almost lost both my Sovas (Those Hoshiko sacrifices were necessary lol).

But the enemy only lost around 140 supply points and retreated. Why?

BECAUSE I HAVE SOME PRETTY HARD BALLS OF STEEL. lol

I've been known to rarely retreat unless I have less than 60 units remaining, so I can preserve the remains of my fleet and boost experience on them. I had at least 230 ships remaining after the battle, not even close to retreating, hell no!

lololol

Explain the ability to get 20 Kols.

Lol

Yes, their Hangars and Aeria Drone Hosts are more expensive and take up ~1.5x the fleet/tactical points of the others, but if I remember correctly, the net cost per squadron is less than the others. Not by too much though.

So the slightly weaker but slightly cheaper Advent squads equal out with the slightly more powerful Vasari squadrons. The TEC squads still suck.

The Ravastra Skirmisher by itself is not tough enough to make up for it's premium pricing vs. the Cobalt and Disciple. After Reintegration is researched(which can be counted as 480 Hull for the Skirm and 720 Hull for the Enforcer), it's so much tougher that it's the most cost effective meatshield as far as LFs are concerned(same thing counts for the Enforcer vs. other HCs).

But still, the Skirmisher and Enforcer both deal poor amounts of DPS for their prices. The TEC ain't much better at this, but the Advent ships are great at DPS/price ratios.

Nope. The Disciple, Illuminator, and Fighter/Bomber Squadrons(via the Aeria) have better DPS/price than their TEC counterparts. The Kodiak beats the Destra here, though.

All the aforementioned Advent vessels top their respective categories as far as DPS/fleet-cap is concerned.

Wow. Interesting... Gonna have to try that.