Somewhat apples to oranges with some overlap.
AH+FX multi-fx including digital eq, multi analog distortion, USB audio, Overbridge, full 1/4” I/O.
Cherie- analog mixer, distortion and compressor, bax style eq. High quality components, slightly annoying minijacks.
Both sound great! Cherie has less flexibility but is a very portable submixer and can be subtle to filthy with no menus or parameters.
What’s best for you would probably revolve around what you want either for!