If you weren't to overcall the river in hand 2, I'd like them both. For different reasons.

Hand 1.
I generally stick to the rule
"If I think I have the bettor beat - raise"
BB being the donk he is I think this is a reasonable assumption. The reasonably passive donk then tells you in no uncertain terms you are behind.
Even if he's stupid enough to semibluff 3bet, there's not too many draws that didn't come in with that river card.
I say NH.

Hand 2.
The only reason to check this, is if you thought you were reverse dominated or behind the BB and wanted to see the river cheaply and have SB pad the pot if you did improve.
The river comes, you didn't improve, a couple of draws come in, the SB bets, the BB calls.....no need to call.

If you hadn't overcalled Hand 2., I still think I prefer hand 1.
I think we're ahead of BB more often than we're behind and letting SB draw cheaply if we are ahead blows.