MK I II III has nothing to do with barrel contour. They were all available with thin and heavy barrel, the slab side didn't come about until the MK II though. The MK I does not stay open on last shot and has not got the small scallops at the rear to grab the bolt handles. The difference between MK II and III is as PoFF says above.
The MK I, II and III were just the chronological progression of this pistol with the noted changes to MKII in 1982 then to MKIII around 2000.
I own a MK I bull barrel and love it. The MK I is my favorite. I have owned a few MK Is and a pair of MK IIs, but have not bought a MKIII. They are all a great pistol for the money in my opinion.