Not by much, the difference between just repeating eye-eye instead of eye-bb is 20 potency. The problem is if the MT is either a PLD or DRK they'll need to swap from their dps combos (which don't have any enmity multipliers except for a small one on Savage Blade for pld) to their enmity combo regularly to keep the lead and for both of them the loss is much greater than what a WAR gains from eye-bb. PLD lose a lot of potency switching RA to RoH, the direct potency loss on DRK is small but more importantly they lose the MP they would've gotten from Syphon Strike if they have to use their enmity combo instead of DPS combo.
Though all of this is assuming the person tanking is actually trying to maximize their DPS instead of just spamming their enmity combo over and over.