They have more in common than differences. Both stress good allignment and learning the fundamentals of good shooting form.
Rick Welch teaches a particular shooting method. He is amenable to some individual preferences, such as shooting with either split fingers or 3 under, but he does have a particular shooting style, and if you want to benefit from his class, you should probably leave your preconceived notions at the door and do whatever he teaches. You can always change things later on if you want to.
Rod Jenkins tends to build more on whatever style you are using, unless you want to change things. Rod stresses a dynamic release and developing good back tension that results in the string hand moving back toward the shoulder after the shot goes off.
Rick doesn't spend much time in his class on back tension, so I think Rod's class builds on Rick's class in that regard. I don't think that Rick would disagree with any of the work Rod does in developing a dynamic release. Rick personally has an unusual release, where his hand kind of flops to the side on release. It certainly works well for him, but he doesn't teach anyone to mimic that particular aspect of his shooting. He stresses a 2 second hold, which translates for many of his students into a dead release, where the string hand doesn't move much after the shot.
Both stress the importance of a subconscious release.
Rick is an instinctive shooter, while Rod is a gap shooter. Actually, aiming is the least important thing either of them teaches, and you could take the fundamentals they teach and apply them to any aiming system you want to use.
Rick mostly teaches one-on-one classes, while Rod mostly teaches groups, but I would imagine they each do both on occasion. In Rick's class, you mainly shoot at normal instinctive distances, out to about 30 yards, while you will mainly shoot at a blank bale at close distances in Rod's class.
I took both classes, and highly recommend that anyone who can spare the time and money do the same.