This has pretty much been beaten to death, but the main advantages I see:
1. voltage drop is much less on higher voltages: you won't be losing power to copper resistance, etc.: thus more available to run the tool. Although, it's pretty much academic at the distances and tools that we're talking about..
2. Heating: at higher amperages that will be seen in the lower voltages, there is more effect from the resistance of the wiring and windings: it manifests itself as heat, just as it will in any resistive heating element.. raise the voltage, you'll lower the amperage, and the heat will go down with it.. heat builds on itself, too: a hotter conductor has higher resistance, which increases the heat, which increases the resistance, etc. etc....
3. Start-ups: when you start a motor, you're basically dealing with locked-rotor amps until rotation actually begins: it'll blow an instantaneous fuse, that's why we use time-delay fuses and inverse-time circuit breakers: it takes a few seconds' worth of the amperage in question to blow the fuse: you'll possibly have six times the full-load amps for a very short time during this period, and that'll make your lights dim, possibly knock out electronics, etc.: a motor that is, let's say 10 amps at 110v and 5 at 220: that's sixty amps startup vs. thirty: that's a significant difference on a 20a residential circuit...
4. available power: the same thing as on that startup, the system is just simply better equipped to deliver that 30 amps than it is that 60 amps: at 60 amps (of course that's a "for sake of argument" figure) your 15-20 amp wiring is heavily taxed and you're losing a lot of power to conductor resistance: it goes away once the motor is rotating, but that's power you could use to get the motor up to speed more quickly, without heating...
5. people don't ask to borrow tools that are rigged for voltages and plug configurations they're not set up for.....
Other than that, it's a wash....