This might help:
BAT = BUG + BULL + some graphics mods.
So they are not mutually exclusive. You can have them share settings because older versions of BUG work fine with newer settings files. Anything it doesn't understand it ignores. The reason you are seeing only five choices in F1 is because it's not finding its settings files, and those are created by default in that case.
It's okay to not share settings. It just means you have to set things up in both. If you do a lot of customization, do it in one and copy the settings (INI files and CustDomAdv.txt) to the other. BUG in the CustomAssets folder stores its settings in My Games / BTS / BUG Mod. Just copy the UserSettings folder into the "BAT Mod 2.1" folder. The F1 settings are in CustDomAdv/CustDomAdv.txt (yes, folder and file name match except for .txt).
I do not know why BAT crashes when you share settings. That is very strange. If it was going to crash, I would expect it to crash when you
didn't share settings since that requires writing settings into the programs folder, and under Vista/7 that's a no-no.