I finally have all three tanks to 60, so I can offer some insight (yay!). Keep in mind, what I'm going to say is based on my own observations, and so is very subjective. Actual mileage may vary.

Paladin - I hate the story of PLD (especially compared to GLD's story, which was excellent), but if you can forgive that, it's a pretty handy tank class. It's easily the most defensive of the three tanks. It can be a little frustrating to watch the enemies' HP barely budge when you use a fully buffed Royal Authority (especially when comparing to the other tanks), but PLD makes up for it by having some utility that can help out the rest of the party, and by being able to actually effectively turtle tank (if you wanted to go that route--check with your group). Clemency, Stoneskin, and Protect add a great deal to your ability to contribute as a PLD, and can help save the group from a wipe. I usually use PLD on new content, simply because it has the greatest ability to support the party in my experience. It's also typically my go-to tank for dungeoning and raiding (though it can be a bit boring sometimes). Paladin also has the best ability of the three tanks to do snap mitigation.

Dark Knight - By contrast, DRK's story is excellent, and hit me right in the feels (though this was somewhat personal for me, and I know that most people won't get that same catharsis). DRK gameplay is interesting, and requires you to pay attention. I feel like I have a harder time juggling cooldowns as DRK, but that's probably just because I'm not as used to them as I am to PLD's. Dark Arts adds a very interesting dynamic, but sometimes makes it very easy to mess up (and somewhat difficult to recover from those mistakes--accidentally lost Darkside and you're out of luck for quite awhile). It does have a good bit of defense capability, but can't do snap mitigation as well as PLD can. DRK also isn't anywhere near as viscerally satisfying as WAR in terms of damage output, but you will notice things dying faster than if you were a PLD. DRK's Int debuff is also handy, but Int-based damage doesn't feels as prevalent as Str-based damage, so this loses to PLD's RoH debuff in my mind.

Warrior - Warrior is easily the most offense-oriented tank, and the one that rewards stance dancing the most. As such, you can output some very big numbers as WAR (Fell Cleavus is real). The job's ability to output damage is coupled by animations that are viscerally satisfying, which in my opinion just makes the job fun. The downside of this is that while WAR has the ability to keep decent mitigation up at all times, they can't do snap mitigation as well (unless they plan very carefully). This might have your healer cursing your existence, especially if you also have a macro that spams them to Esuna you after Berserk. I usually use WAR for Trials, because it helps them go a bit more quickly, and most Trials in the Trial Roulette don't have tankbusters severe enough to worry about snap mitigation (I just cry a little if I get The Chrysalis or Final Steps of Faith, and let the PLD or DRK tank). WAR also has the benefit of being the only tank where I can actually see my DPS contribution on the boss' HP bar.

I can't really speak to savage content, as I haven't raided that difficulty yet (outside of 2.x content), but I fully expect people to disagree with my opinions.