What advantage does a bigger mig welder have with higher voltage? I understand the longer duty cycle part, just wondering if the voltage makes a difference?

I've always stick welded in the past, so setting a voltage and wire speed is new to me. Setting a current like for stick welding is all I'm familiar with.

Comparing the output graph of volt/amp chart on the millermatic 211 (~ 21V @ 200Amps) versus the millermatic 212 (22V @ 210Amps) versus the millermatic 252 (28V @ 200Amps), what is the advantage of having a higher voltage at the same current?

Is the higher voltage simply needed to run thicker wire at the same current as the next thinner wire? If so is there a recommended voltage range for various current levels on different wire thicknesses?