I'll go ahead and throw out the problems I see with Paladin as of 1.21
Firstly, 1.21 "fixed" cures overhealing (healing a target for more hp than they were lacking). This effectively nerfed Paladin's ability to hold threat with cures because more often than not the Paladin's own heal won't hit themself until their healer has already topped them off. Since many boss mechanics can take half a tank's HP off, no healer is going to let a tank ride at 80% hp for the tank to top themselves off for more enmity.
Next is Defense. I've seen evidence that Defense has scaling returns once you near the damage floor for a monster. The problem is that that damage floor is far too high for bosses such as Ifrit (from what I understand one would need 1900 defense to hit Ifrit's damage floor and see their defense actually knock significant amounts of damage off). I am under the impression that Paladin is supposed to be a tank which tanks through enmity generated by abilities and self cures and utilizes higher defense and damage mitigating abilities to take less damage despite its lower HP than a Warrior. Warrior is supposed to tank with higher damage and a larger hp pool, but takes more damage from attacks. This is not how FFXIV currently operates. Your only viable defensive stat in the game at the moment is HP: defense does not do enough, nor do Paladin's abilities. Do you think people would pick a Warrior tank over a Paladin if they both held the same amount of threat while Paladin was taking 1/2 or 1/4th the damage the Warrior did?
Following that, I'm not sure what I can say about AoE tanking other than Warrior is far superior in this too. I do, however, feel that it is actually appropriate for a warrior to be better at holding multiple monsters as it is a separating factor in the tanks abilities. However, when you introduce lots of multiple-mob fights and party grinding, Paladin really gets left in the dust for the superior AoE tank.
A fix in my eyes for the overhealing problem would be a trait reminiscent of a later White Mage trait which made their cures apply stoneskin to the target. Essentially, why not change a Paladin's self-heals into a sort of shield heal which would heal them for a certain amount of HP, but if it caused any over healing that lost healing would be converted into a stoneskin-like shield that would absorb that much extra damage, and would cause full enmity generation even if "overhealing" occurred. I would say not to let a Paladin's heals apply this shield to anyone other than themselves, however. This would not only fix Paladin's threat generation through healing, but also give it further damage mitigation.
With Defense, the damage floor needs to be adjusted where well-geared Paladins can achieve or "cap" defense for a very solid amount of damage reduction, while a well geared Warrior should be able to come close but not achieve it. You can decide for yourself if you want Monk to be able to get close to that and tank, or be an evasion tank, or not able to tank at all. Stats such as Defense and Block need to actually matter enough to where people will materia for them or use food, rather than HP being the wonder-stat for tanks. If HP decides the better tank, nobody will ever use Paladin over Warrior.
Finally, there needs to be some type of balance for Paladins being useful in multiple-mob situations. I really think the trade-off here is a Paladin should be fully capable of holding hate on multiple monsters as much as a Warrior does and take less damage, while a Warrior can hold hate on multiple mobs, take more damage, but deal lots of damage to those monsters and kill them quickly. If you balance it that way, you'll drop down to preference... though in the end even on a single target mob, if you have both tanks surviving the same and holding threat, you'll take the one that does more damage no?
Hopefully this has decently outlined some of the big problems I see with Paladin, and is mildly useful to somebody (preferably the Dev team, though I doubt with my luck they'll ever stumble across anything I post).