I think the reason people think that WAR is so much greater than PLD in damage is that WAR can push larger bursts than PLD. Berserk/Unchained/Maim/Storms Eye/Internal release is not something a PLD can compete with for burst phase damage. In reality their damage output over time is comparable...but the burst-y nature of Warrior damage makes it a bit more visible.

It's one of the reasons I like WAR. It's less random with storms path/Inner beast so I can choose when I want to "block" big attacks. And I can also plan to help during burst phases.

What I can't do as WAR is stun lock adds, or round up all 4 wave spumes and pop hallowed ground to take one for the team. So on Leviathan ex I prefer to go PLD. I feel like I have more control over the success of the fight. You can still handle those things without a PLD tank as a WAR, it's just easier with PLD.