Warrior is arguably equivalent to PLD if you assume that they sit in Defiance and use IB frequently.Otherwise, no, they're miles behind. Something to keep in mind when discussing tank stance is that WAR is the tank most heavily punished for being in theirs. This is why their ability to stance dance has never been a real issue. A Warrior in Defiance loses access to their best damaging moves, does 30% less damage on every attack, and loses some % of crit between 1-10. Compare this to a PLD who loses Sword Oath (Last I checked an approximate 10% of their damage) and an additional 15% off each ability while still retaining access to their entire kit. Even with how much less affected PLD is by Shield Oath than WAR is by Defiance, you still ideally minimize time in tank stance always.
Realistically, WAR is vastly behind PLD in their defensive kit. They are vastly ahead of DRK due to an abundance of tools with low cooldowns, but PLD brings far too much to the table defensively. Something to keep in mind that many don't realize as well, is that fundamentally WAR's tank stance is the worst from a defensive perspective as well. This is due to the benefit not taking immediate effect upon swapping. If, for some reason, PLD/DRK need the extra mitigation to survive they can quickly swap into tank stance and receive the full weight of their stance. A WAR swapping into Defiance needs to be healed for their stance to accomplish anything.
To answer your question regarding DoTs you're overlooking a really valuable aspect. A DoT can be applied during a buff phase for your party and it will, for the full duration, receive the full benefit of every buff. Apart from this, DoT's are the most effective DPS tools because in order to be worthwhile they accomplish far more than a single ability ever can. By the nature of a DoT you need to be rewarded for maintaining it, which means the damage potential is far higher. If you want a simple example of thi, let's compare a PLD's Goring Blade under the effect of Fight or Flight to a Holy Spirit in addition to Requiescat.
Goring Blade - 250 Potency
21s DoT, which ticks every 3s for 60 potency resulting in 420
Both of these are affected by Fight or Flight, adding additional 25% damage, or an extra 167.5 potency
Total - 837.5
Requiescat - 350 potency
Holy Spirit - 400 potency
Requiescat bonus Damage - 80 potency
Total - 830 potency
DoTs do frequently work when the boss goes invulnerable, it's about 50/50. It's really inconsistent, but this is just an example of a DoT with only self-buffs. Add the multiple effects that can impact Goring Blade and it suddenly outshines PLD's highest hitting attack by miles.
DRK is far worse in SB than PLD ever was in HW. If you ever agreed with complaints of PLD then, then you should be able to appreciate what DRK is going through. DRK does pathetic damage, lost the complexity which appealed to so many players, lost its niche as the magic damage tank because PLD gained blocking magic damage, functionally received 2 unique new abilities while losing a ton, is unbelievably dull, and provides no valuable utility apart from Darkest Night (Which WAR just got a better version of). Compare this to HW where the only real problem PLD had which prevented frequent use is how cripplingly difficult magic damage busters were to it.