River plays comes down to a huge range analysis. You need to make some assumptions about the player given your stats/reads. Is this villain likely to still call a river bet with his Jx hands? If so, how many combos is that? How many combos of draws do you think is in his range? Given his range do you have enough equity (>50%) to value bet? If so, then a value bet becomes +EV, but it doesn't mean it's the best play. Checking could hold my value in that he is might be likely to bet worse hands with a higher frequency when you check to him, than he is willing to call your bets with worse hands. If this is the case, and given pot odds he gives you on a check/call, then that might be the appropriate action.

It's really all dependent on the assumptions you can make about the villain, and what's left in his range on the river (would he flat his completed draws on the turn or not?).