What if 'He hit the stick on/against the table.'?
I read a grammarian's explanation that the expression of 'hit the tool on/against something' is natural when it is not a lot affected by doing some action with the tool.
Well, that's fine -- but the table would normally be stronger than the stick, not weaker (depends on the stick and the table, of course). I think in your two examples, the first word is probably the focus for the reader: the vase, the stick. But it doesn't have to be. It's all back to context