You should play whichever one feels the most fun to you. The tanks are currently all quite well balanced. The answer to "Which job of [role] should I play?" is always "Unless you're raiding hardcore, it literally does not matter, and if you ARE raiding hardcore, then you should slot into whatever role makes the most sense for your party composition. Leveling jobs is easy."With that said, here you go.
Who's best at what / What are their pros and cons:
PLD - Really easy to use competently. Generally, has the best survivability due to its shield and curing capability. Has the largest number of actions, so hotbar space can be an issue depending on how your UI is setup.
WAR - Great burst damage. Easiest to swap between tank and DPS stances due to them being off-GCD. Easiest to hold hate on dungeon trash due to all of its "hit everything" actions having a stupidly high enmity modifier on them.
DRK - Requires the most skill to play. You'll be hitting buttons a lot more than the other two. That's usually either an easy sell for why you'd want to play it, or a dealbreaker for why you don't.
Who has the best magic/physical defense:
PLD generally takes the least damage due to its shield. Aside from a single DRK ability that reduces magical damage, there's little difference between physical and magical damage. Hardcore raid groups tend to like having a WAR since its "I can't die" button (Holmgang) has the shortest cooldown (3min) compared to PLD (Hallowed Ground, 7min) and DRK (Living Dead, 5min).
Who's the best at aggro:
Aggro is so easy to hold, this question is irrelevant.
Who's most desired:
I generally hear the most complaints about DRKs, but the difference is minimal. I think DRK tends to get a bad rep simply because it takes more skill to play, so it's easier to encounter bad DRKs.
Who has the highest DPS:
The last tank assessment I saw showed them all within 1% of each other. WAR definitely has the highest burst damage though.