I'd say the short stacked situation is the best to continuation bet. You're a lot less likely to get bluff raised (because you've already committed) or called by an inside straight draw. If you're deeper, you can more likely get a pair of kings or a pocket pair to fold, but it usually takes more than the one bullet.
I'm inclined to c-bet a lot in any case. The BB should have a large range in this spot, because you made a raise from prime stealing position, he was closing out the action heads up, and he got a discount in the BB. Against a wide range, that's a very uncoordinated flop.
The one downside is that it kind of looks like he's defending his blind. If that's true and he's anything but short stacked, he's going to bluff check-raise a lot of the time. So it depends on the player. If he's aggressive, I would rarely c-bet this unless he's short stacked.
Edit: If you might c-bet again on the turn versus a call, then I like c-betting the flop against a deep stack better.