On the surface, bet/folding looks better because folding to a river raise is super easy. That doesn't mean it's better than check/fold. When you're called, there are way too many more hands that beat you. You lose to AQ, A3, A4, 22-QQ and only beat A6-AT when called. Betting is definitely worse than checking here.

The real question is does checking warrant a call? It looks like this guy will only bet monsters, big kings or busted flush draws that didn't pair. He doesn't have a monster that didn't raise the turn too often, so that only leaves A5 and 33 for huge hands on the river.

Although it's close, I'd lean towards c/f over c/c here.