Between gaming and entertainment modes there is little difference. Both modes use EAX and CMMS (if you want them) and have global resampling enabled. The differences seem to be limited to pretty narrow things like the kind of EAX available (gaming uses EAX for general gaming, entertainment seems to have a more home theatre related set) and DVD-A playback.
Gaming mode is the mode most analogus to the way previous Creative cards operated and is a good general purpose mode. I leave my card in gaming mode 99% of the time.
The mode with a difference is audio creation mode. This dramaticly reconfigures the way the card works. The biggest difference is that it shuts down the resampling engine so output is bit matched (and can happen at different frequencies). It also turns off EAX and CMMS, and uses that engine to do effects sends instead. It also offers you individual routing control over all your inputs and playback channels in all modes. Finally, it's the only mode with full ASIO 2 support.
Basically it turns in X-Fi in to a pro audio card. Thus I use it when I am doing audio creation or mastering.
If all you do is gaming and music listening, you can set it to gaming mode and forget the others exist. The only thing that might intrest you about audio creation mode is you can use it to get bit matched playback. If you switch the card to AC mode and use ASIO or WDM KS as an API, the sound comming out will be bit accurate with the orignal.
All well and good, but highly overrated. I'd put money on the fact that you can't hear the difference between a non-resampled and resampled signal with the X-Fi's excellent engine, and the other effects you can turn off, if you wish. However, you may find, as I do, that the effects like CMMS sound good and you want to leave them on for music as well.