I think SoboLAN gave a lot of great analysis in his answer. There are two major things that I have to add:
With 10 outs, we have about 35% equity against most of our opponent's range (excluding, obviously, the hands that we are already ahead of). That's nothing to sneeze at. If there were no more money behind, we could expect a positive return on calling a pot-sized bet.
Looking at our opponent's stats, I have to guess that he's 3-betting around 12% in this kind of button-vs-blinds situation. That's a little bit tighter than any-pair-and-any-broadway. With his aggression factor, I do think that he is going to c-bet almost every board he 3-bets, regardless of how well it hits his hand. The bet-sizing itself doesn't tell us much, but it makes me slightly inclined to he wants a fold.
Against that entire 12% range, pokerstove puts us as a slight favorite here at 53%. Certainly the first hands to discount are going to be the ones that we are ahead of, but I can't see us with less than 40% equity, and I seriously doubt we are less than 45%. Given that, to me, it seems like a crime to fold.
I know we don't have much history on this opponent, so street-by-street aggression numbers are probably pretty sparse. Still, if we have seen any indication that he is mostly aggro on the flop and slows down on the turn, then that argues for a call in my book. We can use our position and our equity in the hand to see profit from later streets.
I often agree with the thought that putting in a quarter of your stack to fold later can be a bad idea, but here I think it's often going to be our best option. As above, folding gives up too much. I do think that calling with position here is +EV, even knowing that it's a large portion of our stack.
The question to answer is whether calling is more +EV than raising. And that depends on how much of our opponent's range we expect to see fold. Even if we shove, he will be getting nearly 2-1 odds, so we probably get called too often for my tastes - we're certainly getting folds from the hands that we beat, but that's not really a huge win for us - we'd rather keep those hands in. That said, let's look at it.
If we assume he calls a shove with 33+ and folds the other 60% of his hands, we're left with about 30% equity (given sets and whatnot). He might also call occasionally with flush draws, but I'll ignore that as it only increases our equity if it happens.
- 60% of the time we win $91+$84 == EV of +$105 from his folds
- 70% of 40% of the time, we lose $400 == EV of -$112 from his calls where we lose
- 30% of 40% of the time, we win $84+$400 == EV of +$101.64 from his calls where we win.
That shows a net of over nearly $100. It's hard to argue that we make more than that by calling, so I shove unless we believe he is 3-betting significantly less hands than I estimate.