Which has a greater impact on your cholesterol levels: diet or exercise

Diet

It depends on the extend to which you follow each. Usually diet will have higher impact. Ideally a combination is definitely better.

Main thing is Burn What You EAT, so exercise is better.
Vice versa is the effect if eat less and burn more, than protein start to burn out from muscle and one looks skinny.
So eat healthy as much as you can burn out.