On the WoW front, I would have to say that if you were to start playing WoW, this (cataclysm) would be the best time to start. Reworked new player areas, and a huge fresh crop of new players means you will have people at your character and player skill level to progress through the game with, which is a great thing.
That said, I haven't played WoW in ages, and have no plans to return. Eventually I just hit a point where I realized that I wasn't having fun. It was more like I had acclimatized myself to accepting long bouts of repetitive action for carefully timed rewards. I lost any sense of immersion.
I immediately found Eve refreshing. It's not that it's better than WoW, exactly. The two are coming from such extremely different directions, and are offering different experiences, that it's really hard to compare them directly. I'll try to cover some of the main points as I see them:
Eve is initially tougher than most MMOs to get into, and getting past that first hurdle can take some time. Partly this is due to the interface, which, while perfectly suited to Eve, is very much unlike that used by any other MMO. Partly this is due to playing within a three dimensional space, which can be disorienting or awkward for some people. Partly, this is due to a lack of visual cues. While the graphics in Eve are nice, you will likely find it much easier to handle combat "zoomed out" to the point where you can't really see individual ships anymore. And partly, also, this is due to the fact that you have nearly unlimited options from day one, but little real guidance. You might really appreciate the wide range of ships, modules, skills, implants, corps, alliances, systems, wormholes, professions... or it might overwhelm you. My best advice in that regard is to join a new-player corporation or a training corporation (Eve University is a good start).
Eve has a bit of a identity problem. The developers, at any given moment, can't decide whether they are catering to PvE focused "carebears" (the majority of the population) or to the PvP focused null-sec alliances and low-sec pirates. This won't mean much to a new player, but I feel it is one of Eve's most defining traits
Eve can pay for itself. You can pay your monthly subscription with the in-game currency (ISK). This won't really be an option for you right off the bat, because you won't have much cash, but if you enjoy the game and are still playing in a few months time, it's a nice option to have. While I don't mine much any more, there was a time when a weekend of off-and-on mining would pay the monthly bill for both my accounts.
Eve is a very social game. And I mean very, very, social. Corporations routinely span hundreds of players, and alliances are often built up of dozens of corporations. Your corp mates will generally be the people you spend most time playing and chatting with, so it's important to find a group you can get along well with. You also want your corporation to be active, and run by a CEO and directors who have... well... direction, and who have the strength of personality and determination to get you there. A good corporation is your support structure. A bad corporation can ruin your enjoyment of the game, so feel free to abandon a sinking ship!
Eve's economy is player-run. WoW and other games have crafting, but in Eve, 99% of everything is player created, from resources that players mined and harvested themselves. I find it interesting to watch the fluctuations in the market whenever an expansion is approaching, or a particular ship is being rebalanced, as miners start stockpiling minerals, and industrial speculators start hiking prices.
PvP, in Eve, generally ranges from small gangs to multi-alliance fleets. Solo PvP is generally ill-advised, simply because your opponent is rarely alone. On the large-scale fleet side, you have hundreds and hundreds of battleships and assault cruisers supporting dozens of capital ships. On each side. A single battle can easily see a trillion ISK destroyed, which translates to tens of thousands of dollars and months of work. It's kind of Epic.
During my time with Wildly Inappropriate, fighting the Russian alliance Solar Fleet (among others), I personally lost a few hundred dollars "worth" of assets. Not that I actually paid for any of it, but Eve has a pretty stable dollar to ISK ratio, so it's interesting to step back sometimes and consider just what any given loss or kill was worth.
This brings us back to the economy. Large fleet fights and alliance sovereignty wars in general have noticeable impacts on the economy. Every ship and every weapon, shield, etc etc etc on each of those ships was built by someone, and each one lost has to be replaced. This keeps the economy going stable in way unseen in other MMOs.
I think that's all I have time for. It's definitely an intriguing game that offers a radically different experience. But it isn't for everyone, and it has a steep learning curve, which scares a lot of people off. If nothing else, give the 2 week trial a go. And for your own sake, ask a lot of questions, and whenever possible fly with others. You'll get an idea for the game a lot quicker that way, and end up having a lot more fun. Trying to get at the meat of the game alone, and in two weeks, is a very tall order.