Okay, let's see..
1) There is a HUGE difference between WoW and FFXI. The only thing they have in common is that they are fantasy based MMORPGs.
2) It works the same as all MMORPGS. You fight/quest and level. Sorry, it's a simple answer, but all the games at their core have the same thing.
3) The battle style in WoW is so much better then in FFXI. FFXI is just click one button, wait until you have TP and then do an ability. WoW, you're constantly doing a ton of different abilities.
There is just so many differences between WoW and FFXI.
My suggestion is to go to the WoW site and read up on it in the Game Info section. That should give you a good idea of what the game's about. Then come on back and we'll happily answer any more questions you have.
There are also numerous threads are about the differences between FFXI and WoW. I reccommend RedmoonXL's and KingJord's reviews on WoW, both being former FFXIers.
I'm a former FFXIer myself, and I say, dump that game and come here.
www.worldofwarcraft.com