OK, I'm a dummy and I have to ask the question, "Why would the choice of the engine affect the characteristics of the output if they are turning the same generator/alternator (i.e., the welder's guts)?"
Assuming both engines are the same horsepower, turning at the same RPM, I fail to see how the welder's arc characteristics would be different. Fuel consumption, maintenance, etc. could be expected to be different, but why would the arc characteristics differ?
As for the arc control, that is most likely varying the slope characteristics of the welder.
Best regards - Al