It's pretty much a way ahead/way behind situation. If you cbet 1/2 to 3/4, only stronger hands call and you fold out air and probably draws, so you get zero value. If you check, you also get zero value from weaker hands like 54s and a call here probably loses against a weird 2pair, hidden set or TT. If you decide to bluff catch, you'd need a read on how much villain is bluffing.
I'd bet 1/3 or 1/4 of the pot as a cbet on the flop. This opens up villains calling range so you get value from worse hands plus if you get raised, or called down, you would not lose as much.
Ergo, you make money from weaker hands and don't lose as much from stronger hands.
The way you played it you make zero money from weaker hands and lose 3bb against the stronger hands. First option seems smarter to me