As much as I hate JJ-Prise, I hate the Vengeance more. It's JJ's version of an Uber ship. It's unattractive and silly to say the least. But I do like the question.
I'm reminded that while the Vengeance did manage to kick the JJ-Prise's behind, it wasn't a fair fight. First, the ship's warp core was damaged. Secondly, since JJ-Kirk didn't think another ship could fire at him while at warp, he may not have had his shields up when the Vengeance attacked. If the JJ-Prise was in prime condition, it could have gave the Vengeance a run for it's money. Or maybe not, who's to say in universe.
The Vengeance may have more phasers to fire, but that means nothing against regenerative shield systems, ablative hull armour, quantum torpedo's and multi frequency phaser arrays. Besides that, the Enterprise-E is commanded by a captain who's been a captain for decades, with just as much or more experience than Admiral Marcus. Picard would win, thus the E-E would win.