RE: 11.1 vs 14.8
Power, with electrics, is measured in watts.
Watts = amps x volts. Therefore, the more volts you can provide, the more power you potentially have to fly.
I don't think I've seen a speed control that will take a 4S battery and allow you to use the BEC (battery eliminator/elimination circuit) in it. You'd have to get a separate BEC to power your electronics, or use another pack.
Some motors may not be designed for a 4S pack--they have maximum RPM's.
If it flys well with a 3S pack, I'd use that.