Two issues: cost and voltage drop.
When you go from 110/120 to 220/240, your amperage consumption drops. Power company charges you for amperage, not voltage.
Voltage Drop: when a motor first starts, it is essentially "shorted" for a very short period. You know "motor starters"? Motor starters are basically circuits that will bypass a fuse or breaker for a very short interval allowing the motor to spin up at very high amperage, then returning "monitoring" to the fuse or breaker.\
Anyhoo...motor "shorts" which pulls a huge whack of amperage. Anytime ANY current passes through a wire, you have voltage drop. Voltage drop is a function of amperage. More amps, more drop. More drop...less amperage (self limiting at a given voltage).
Your friends' perception of higher acceleration derives from this phenomena. During the short spin up cycle, 220vac delivers more available high amperage because the OVERALL amp draw at the higher voltage is lower, so the drop is lower and so the amp limiting is reduced.
Now... there is an underlying assumption here. You get all your 220vac performance improvements IF you wire with wire sized for the 110vac hp requirement. Voltage drop is a function of amperage AND a function of the wires resistance. Resistance at a given voltage goes up as diameter goes down (think, water pipe). Go with the smaller diameter (220vac amperage rated wire) and now your voltage drop at startup (inrush it's called) is basically the same as your 110 scenario.
One of other benefit. The heat produced by a motor is a function of the SQUARE of the current used. The current used is a function, of course, of the load--but what most people don't get is WHY. When you load a motor, it wants to slow down--this increases the angular distance of the magnetic field in the rotor to that of the stator. THIS causes current to go up---which brings more force into play (thus the motors tendency to speed back up) but produces MUCH more heat.
So....if you have, for example, a 1hp table saw you won't notice any appreciable difference in performance if you are ripping 3/4" Eastern Wimpy Pine. On the other hand, if you are ripping 2" bubinga, on 110 you'll trip the thermal overload on the motor every 5-7 minutes of cutting. DAMHIKT
Switch to 220, and the thermal overload problem because much less prevalent. Needless to say, a cooler motor is a happier, longer lived motor.