I'm not 100% sure I understand the question.
AFAICT, the only thing an AppleTV can do that a Mini can't is act as an AirPlay client.
As for the reverse, the Mini can handle all the browser/Flash type stuff that the AppleTV can't: Pandora, Hulu, etc. It also has storage, and the iTunes visualizer, which looks nice on a big screen.
I didn't intend to replace my (original) AppleTV with the Mini, but that's how things worked out, and I'm very happy with the results.