Think of it this way - your motor for the pump draws the same amount of power (watts), Power = Volts * Amps. So, using half the voltage will require twice the amps (the power draw of the motor is going to be a constant for all intents and purposes) . In real world terms - (as an example) - my pump runs on about 1400 watts . I run on 240V, so the amp draw will be 1400/240 = 5.83 Amps. Running the same motor on the same load on 120v would be 1400 / 120 = 11.7 amps. The wire needed for a 240V run will not need to be as large as the wiring for 120V for the same pump, and the 240V should be less susceptible to voltage drop over a run of wire.
You SHOULD be using GFCI breakers for your pool equipment, for everyone's safety. This is where 120V has an advantage. You can find 240V dual pole 240 GFCI breakers, but my GE 20Amp ran about $90-$100 - compared to your typical 120V GFCI breaker being about half that.
