What actions are performed by Install OS X Mountain Lion.app that are not performed by InstallESD.dmg without the app?
My working theory is that there are no meaningful differences in actions performed under the app as opposed to the DMG.

One could argue at a low level that the difference is that invoking the Install OS X Mountain Lion.app bundle loads app and UI frameworks that simply mounting a DMG does not, but that's not exactly the intent of your question I'm sure.

Any meaningful installer-level actions should be identical in either medium, since the majority of the resources are in the DMG, and the DMG is in the app. The app must mount the disk image in order to get at the necessary assets.