Heres my take on this from a DRK main, I've barely played Paladin, I do not like playing the job, but I have nothing against those who do.
I've cleared up to P7S last week, all in party finder. Played with every combination availble to me and honestly I think that PLD is the one I'd think struggles the most, but not for damage reasons surprisingly. (or at least not ONLY for that reason)
The thing I found to be most cumbersome when playing with a PLD is the fact that their Invul's cooldown is 7 minutes long. And while I get the idea that its like that because its invul has the strongest effect, I feel like the expectations of an invul skill are different from what they used to be.
They're no longer "Oh fuck, Emergency Tank Privilege" buttons, but rather expected parts of your kit to be used at certain times to make mechanics go easier. This raid tier really stresses it with its excess of heavy DOT effects, ESPECIALLY P7S.
Beyond damage, there is another aspect of this game that isn't talked about as much as it probably should, and thats resources. By that I mean, defensive cooldowns, healing, mitigation, you name it. You only have so many so using the bare minimum possible is ideal for longevity, which leads to even higher damage.
Simply being able to only deal with those heavy bleeds on ONE tank opposed to two is huge, taken further by the fact that now the other tank can funnel their cheap mitigation into the tank with the DOT. TBN specifically is amazing for easing the pain of these DoT Debuffs, making them much less stressful on your team.
Simply put, if you have a WAR and a DRK you can alternate these bleeds pretty well and still get your invul back at the end of the fight. GNB is also fine. All of these tanks can comfortably use their invuls in cycles.
PLD can do this as well but really only once per fight, and I think thats a pretty big detriment compared to others which can safely do it twice. Theres a prevailing strat for P7S thats pretty similar to ELMO that uses both tank Invuls, PLD cant do it and also take an invul during the beginning of the fight due to that 7m CD.
This will become less of an issue as gear power creep continues, and good players will be able to bypass all of this no problem. But from week 1 with PF clears. My experience has been that PLD really isn't optimal offensively or defensively.
A lot of the unique defensive tools that PLD have honestly have too many strings attached to be useful, to the point where DRK's incredibly simple defensive utility of being flat mitigation low cool down (Oblation/Dark Mind) seem more fitted for raiding than PLD.