If I had to guess which game you'd like better - I'd say WoW. With 11 million subscribers and counting, this is not a wild guess.
First of all, let me start by saying this: There's a reason your Google search went the way it did - and that's because no one has any need to argue why WoW is better than (place MMO name here). It is a hugely fun game, and I have met many people who I couldn't even imagine sitting in front of a computer, let alone a computer game, who play wow. I even convinced an old girlfriend of mine to start playing - and she loved it.
WoW lets you assume the persona of a hero in a fantasy world, dominated by magic, good and evil, and two warring Factions. You directly control your character in the third person, level him up, collect items etc. If your hero is slain, your spirit appears in a graveyard, and you must retrieve your body, with a slight penalty which only lasts a short while.
EVE, on the other hand, gives you control of a spaceship, and places you in a galaxy in the far future. You level up as well, though training skills takes less than an hour at first, play for a few days and you will soon see that it can take actual weeks (as in, real-life weeks) to learn a new skill. PvP is completely unforgiving -you die, you're dead. You lose stuff - permanently. The economy is huge, the amount of items staggering.
Both are very different games. Both have their advantages and disadvantages. But they do have something in common - both are MMO's. This means that both are online traps. They can consume huge amounts of your time, without you ever getting bored. You will find yourself making excuses for to play it!
I played WoW on and off for about 4 years, racking up huge amounts of play time. Do not take all the controversy about WoW being addictive and destroying lives etc lightly. It happens, and it can happen to you. And the worst part? You won't even know it. And when you do, you won't admit it to yourself.
WoW is very addictive. It is designed to keep you coming back, to always give you something to do - and reward you for it. If I were to recommend a game to you, I wouldn't recommend an MMO, period. Surely there are other games out there that have sparked your interest. I don't mean to tell you how to live your life, but if you find yourself with huge amounts of time to burn, don't turn to MMO's.
As it stands, the decision is entirely up to you. Both games have a free trial period. Why not try them both out for yourself?
edit: Lord of the Rings Online is a fantastic MMO - casual, fun game with a mature, friendly player base, but the real plus is that it won't hook you like WoW will (A good thing!) . I highly recommend it.