What is the difference between Gnome Compiz Flashback and Gnome Metacity Flashback?

The backend is different: Compiz uses a 3D compositor to display the windows. Whereas Metacity displays the windows in 2D. So if you have a low end graphics card and/or want to save energy on a mobile device I would suggest that you use metacity.

There also used to be problems with 3D applications in combination with compiz.