The method(s) you use to control AmpliTube will have no effect on the actual tone that you get out of it—regardless of whether you use a mouse or a complex foot controller with four expression pedals, it will not influence the sound at all. However, it will have an effect on your control of that tone.
When recording, you may find yourself in a situation where you are limited to one track for whatever reason. (Yes, it can still happen in this digital age.) Being able to switch sounds mid-track can be difficult, if not impossible, with merely a mouse and a spacebar. If you have all the tracks you need, you can potentially get by with just a mouse—but what about wah-wah and whammy effects?
This is where MIDI control comes in.