EVE Online and WoW have similar Elements. Both are extremely loot based. Both have world PvP. Both have crafting. I think that is where similarities end.
EVE is balanced for PvP, not PvE. Period. The EVE devs want to make sure the PvE is there to support the PvP, not the other way around. They also want it to be group based. There is some PvE that you cannot do without help.
EVE has alliances, think of this as a band of Guilds, that have their own war system.
EVE has PvP looting, thus, their are severe rewards and consequences to actions for player combat.
EVE is bigger. Period.
WoW has no real death penalty in PvE or PvP unless you consider fixing your gear or travel time a penalty. I do not, its merely a bathroom break from the action.
WoW's crafting system is a babies toy compared to EVEs.
WoW's epic gear, comparatively, cannot hold a candle to EVEs ultra gear.
WoW's market is only half done. Bind on Pickup gear ruins an attempt at a completely player driven market.
WoW does have a character akin to traditional MMORPGs. You walk, run, fly, swim.
WoW's music is more epic and heart pumping. EVE's is more embracing and relaxing.
WoW's features are fairly upfront and at some point easily grasped in a week. EVE has features so esoteric n00b is a term you will use for yourself in some way or form for years on end.
Depth... WoW cannot touch EVE.
WoW has a steep requirement for is end game PvE. You class choice can make you or break you once you reach lvl 60. Warriors and Rogues have a hard time finding homes for end game simply because they are overplayed. Try and find an end game guild with a warrior if all you have managed to loot are blues.... I dare you. Rogues... well.. good luck finding anyone to take you if you aren't grandfathered into a guild based on local or strong pre-WoW friendships.
WoW's world PvP is underplayed. Battlegrounds has turned WoW PvP into Unreal Tournament. This is the casual player's true endgame.
The level of commitment. EVE lets you train offline. All that is required to level in EVE is you obtaining ingame credits, called ISK, and buying the skills. WoW requires you to kill stuff and/or quest.
WoW has a good set of quests. EVE missions are more repetitive in a sense, because this is not EVE's strong point. However, you will not run every mission in EVE fast. You won't even be able to solo level 4 missions until you have 4+ months of game time under your belt. WoW's quests, once you run through 60 with 1 character do tend to be repeats just from a differnt race angle but are different enough to not really complain. PvP is inevitable during questing or missions ( on WoW PvP servers.)
Wow has rested XP. This is a casual player's godsend.
WoW is grossly imbalanced but is getting better. EVE ins't grossly imbalanced at all. Whiners will always exist in EVE if they loose to x,y,z but it's just whining. It is easy to adapt in EVE and those who don't or can't like to cry. The DEVs usually don't listen to them... Blizzard on the otherhand.... well look at Rogues.
Both will give you some similar elements. Both are great games. It really boils down to how much time investment at the end game you have for WoW and how much imagination you have with EVE. Those with little imagination will find EVE bland... but in reality it is just them.