The Mark III was the first 3 channel tube amp that evolved from the 2 channel Mark II. They sound amazing but suffer somewhat from the lack of independent EQ and volume controls for each channel. As a result, a Mark III requires some trade offs in a live setting. Really good crunch in R2 means the cleans suffer and vice-versa. (Remember this is the first time ANYONE attempted a 3 channel tube amp. This amp was truly groundbreaking despite the relatively small issues.) One of the more annoying of these issues is the difficulty balancing volume between R1 and R2. However there is an easy mod to add a separate R2 volume pot on the back of the amp and solve the problem.
The Mark IV essentially took the 3 channel idea to the next level by adding separate eq (almost), gain, presence & master volume controls for each of the 3 channels.
EDIT: The stripes are simply the various revisions of the Mark III circuit. I'm not going to get in a debate about the which is better or worse. Search that topic and you'll find PLENTY of discussion.