Very broad question, I guess the usual answer is "it depends".
More specifically I'd consider how aggressive villain is, ie will he be bluffing alot (or value shove the same or more hands than he'd call with) if we check? Will he ever check behind a better hand? Will he ever fold some better hands if we shove? Will he call worse?
In general I suppose it's better to shove yourself because most villains call more often than they bet.