I just switched out all of my Miller mig machines for Lincoln machines last year. Don't get me wrong, they both make great machines, but I had all early 350P's and they all have motherboard problems that the Miller rep here didn't want to deal with, so off to the Lincoln rep for all new 350MP's it was.
Now, for both of the welders you have listed. They're the exact same welder. Owned by the same person, and build in the same place, using the same specs. The difference? Hobart machines are tapped and Miller machines have infinite controls.
This means the Hobart has a certain number of "taps" or settings that you can turn the wire speed and voltage to. The Miller however can be set to any number you want, making it infinitely variable.