[fizzleboink]

I don't see villain calling a bet from you with a worse hand (Q high). Unless you have a read that says otherwise.

Other Ace highs are probably calling the river but that doesn't give you any value.

PP's like 77 will call, and will probably bet the river if checked too (majority of the time).

There's a very small chance that the villain is slowplaying.

Checking might induce a bluff from a worse hand, although that is also very unlikely due to his aggression.

So overall, I don't think it makes too much of a difference. Although I think check/calling is maybe slightly better.