As a side note, I called Hobart and asked what the wiring specs are for the Iron man 230 and they stated 50a on 6g wire. I wired my circuit based on these higher demands relative to the specs of the compressor.
I wonder who you talk to there, the Hobart as well as most welders with a 50A factory end will run from 10 fine and may call for 8 if its in a cable. For the original poster has some free 6, free is good, 6 is great, would probably install a couple circuits if I had the material. I used mostly 6 as I already had a roll on the job, if I didn't and had to buy it would have been 8 and I wouldn't have sweated with 10 as they are all single circuit in pipe and very short.
These lighter wire circuits are fine for home welding equipment, I always prefer a size above the minimum for sure. I also keep in mind they are welder circuits and if I was to install something specialized would pull a cover, check the connections and verify that the wire size was adequate for the equipment I was hooking to it.
The 230 has demand similar to a buzz box but longer duty cycle at rated load. You can crank it above that but it wont be done in small hobby or maintenance shops. I think it falls right at the limit for a 10 cable, the notes say it may need to be up sized but I believe this particular machine may slide under this,,, possibly not though due to duty cycle. Not exactly where the nema numbers,,, etc are.
Some of the small units, 200 compact class allow for a wire smaller than the cord size, when doing so there is a smaller max limit breaker, even though this circuit may be work and be legal no one thinks its a great idea. Same for a buzz box wired with 12, v drop can become an issue and its easy to run these past their duty cycle on occasion. Putting larger wires in may be beneficial especially if this circuit may be used for multiple machines. In a perfect world a 50A circuit is single conductors in pipe, single circuit.
I put a 25 ft 10 cord to a 250 class mig the other day, was going to thermo read it but sat down and weld constant for 20 mins, grab the cord, couldn't tell it warmed it by feel thats for sure. Near 40A down it about as steady as the operator could use it.