ent is right, it all seems like switching engines.
But whatever reasons are, here is some information about where personal data is stored:
Settings, including keybinds:
Jedi Academy\GameData\MBII\jampconfig.cfg
Jedi Academy\GameData\MBII\openjk.cfg
My Documents\My Games\OpenJK\MBII\openjk.cfg
Achievements:
Jedi Academy\GameData\MBII\achievements.dat
My Documents\My Games\OpenJK\MBII\achievements.dat
Which path is actually used depends on engine you choose.
More over, it's also important how Movie Battles is getting started, via MBII Launcher or via .bat file; I've got a feeling that Launcher pass some additional command line parameters those affect the directory for storing data.
You can also consider storing binds in separate file, and execute that file from base config, like Gunman121 suggested.