> Intuitively, I feel like weighty hits tend to drive the nail into the wood, whereas fast hits just bash the nail about. That might be more about accuracy though?

Yes, if you're using your arm, there's a tradeoff between speed and accuracy. If you're using a nail gun, not so much.

I was just saying that it looks to me like measuring what happens in energy seems correct, and measuring in momentum looks like a conceptual mistake.