Ruben Bakker

Between the 2 hands mentioned there is roughly 1% difference in equity (advantage to AJs) when they are up against a random hand.

65.39 vs 64.43

Playing with caution to me would imply checking back the turn and probably calling most riverbets, depending on size or what card comes. There could be a scenario where I would fold to a riverbet after turn check check. Another thing to think about is your call preflop given your assumption that he would only 3-bet premiums and some broadways. That would mean that in a fair amount of the cases, if not all, you are up against either an overpair or against dominating hands. Not he best scenario possible. Then again it is a lot to ask to fold this hand preflop IP. But back to the hand... I think the correct play is to just check back, you dont really have a hand that can stand a c/r either plus I expect to have great showdown value since he didn't bet flop. If the turn would be a second heart I would definitely be more inclined to bet.

Btw... how much did he raise on the turn, can't find that in your HH