I'm only familiar with the Mark IV from recordings, live music and stem tracks. I have never played a real one, but what I can say is the Mark IV models n the Axe FX III are my favorite in the unit, which is saying a lot because I love so many models. They give me the sound of a Mark IV I have heard very easily and it feels phenomenal to play. I only play at home, so having a real one doesn't make sense. At this point I wouldn't want one though (unless it was free!) because the Axe is just so damn good. Add the effects, and it is many, many cuts above anything else on the market.
If I get a chance, I will try to post a clip of the Mark IV model sound.