A lot of job classes in FFXI and WoW, you can draw direct correlations between them.
Warrior - Warrior
Both are highly effective melee DDs, given the right gear. WoW warriors have the advantage of a Rage meter, and a -lot- more abilities to use, making woW's warrior more interesting to run.
White Mage - Priest
Both are the top of the line healers for their game. Whitemage has the advantage in the healing department; they have a wider variety of remedy spells to deal with curses, poisons and the lot. Priest has an edge in damage; A whitemage attempting to do damage in a party is laughed at.
Redmage - Druid
Both are Jack of Trades; both have abilities spanning all classes.
Redmage loses melee viability with higher level, and falls into a specialist Debuffing class. Druids can effectively "be" most classes, but can't compete directly with said classes.
Blackmage - Mage
Both are masters of elemental damage. Blackmage has an edge in crowd control, through use of AOE sleeps. Mage has an edge on crowd control through damage, having AOE spells that don't require you to stay still. Both are glass cannons, and will shatter with an appropriately placed ping.
Ranger/Beastmaster - Hunter
Rangers and Hunters both have the advantage of a strong ranged attack. Rangers have higher damage per arrow; hunters have more special abilities. Beastmasters and Hunters share a mastery over animals, and both control pets that do much of the fighting for him. However, Beastmaster pets are only temporary, and will turn on their master unless properly released from service.
Paladin - Paladin
Similar to what I said about Warrior; these classes are nearly identical, being heavy-duty tanks with moderate healing ability. WoW paladins have a wider spread of combat abilities to use.
Thief - Rogue
Again, similar to Warrior. Identical in purpose; Rogue gets more abilities to choose from, in addition to the whole Combo Point system.
Thief adds a new tactical element to the party with Trick Attack, which fools the enemy into thinking the next attack is comming from whoever the thief hides behind. Crucial for hate control during long fights.
The other jobs don't have quite so direct correlaries drawn for them, but I'm sure if you try hard enough, you can find connections.
However, before you make your decision on which game to play, you should be -very- aware that WoW and FFXI are two very different games. WoW's jobs can be solo'd clean to the last level without too many problems. FFXI is extremely group-oriented, requiring parties of 3-6 players to level, and up to 18 players to do some quests. Endgame for FFXI is tedious, mostly revolving around camping and fighting monsters that only spawn once a day, or worse yet, have 3 day long spawn windows. If not that, then fighting in special zones that you can only enter twice a week, for three hours.
WoW, on the other hand, I hate to say, is populated 80% by people of low standards and quality, many of them runoff and refugees of FFXI who couldn't handle the cooperation required. As a result, you almost can't rely on a pickup party to get the job done, and in a way, this forces you to rely even more on your friends than FFXI does. It's also heavily PVP oriented, which can spawn some horrible attitudes, and e-peen stroking circles.
Sorry for the long writeup. But it's very dangerous to choose one game over the other without an extensive knowledge of what to expect.
Personally, I'm torn. FFXI's party atmosphere is great, and the tactics it requires on a regular basis is refreshing; however, many of my friends have left the game for WoW, leaving me with very little to strive for. And I won't say it isn't a nice change to be able to solo, or duo with my mate.
There's my two cents, and if you bothered to read all of it, I congradulate you. =3