Watts are watts. With a higher voltage, you can use smaller wire. I run 220 for most things for branch and breaker size. Tiny less drop in the lines maybe give a slight start up advantage, but as under start up, the load is less than working, so not that big a deal. Maybe you could measure stable speed being a couple hundred milliseconds quicker. and drop cord much cheaper in 12 ga than 10 ga.
The mag starter, if only a starter, has nothing to do with motor control or current. It is a self-latching relay. Nothing more. It is held on by the current so if power drops it will drop and not come back on until you tell it to. Now some starter/control boxes have breakers in them, thermal delays, remote control, and such. Do not confuse a simple mag starter with a mag control box. Size and price are a dead give away. A mag switch can be $20, a mag starter control box several hundred.
You can buy stranded outlet box switches RATED for motors. Regular wall switches are not. Read the specs. My compressor is on a wall switch, properly rated. I bought mag switches with big paddles so they are easy to bump off rather than fumbling for a small switch.