I advocate betting out. It's doubtful that in such a large pot someone has a Jack. A flush draw may very well bet out for value in this pot on the flop, as chances are one of the flush draw cards is a Ah and the other one may very well be Qh. AA- 1010 is betting out before you by now, you risk getting raised by AA-1010 behind you (but with size of the pot you're EV is still just fine). Only AA is a horrid alternative at this point, can't worry about that.

Balance that against the fact that if you bet out, you may get a cheaper card, I bet here.