I've been to both Rod Jenkins's and Rick Welch's classes, and they are different enough that it would be nice if you knew which style you liked best before you went. The catch is, I don't know how you're going to do that, because even if you read about their styles on TradGang and watch their videos, it's not the same as being there. Either one is going to explain things to you personally about your own shooting that they obviously can't do while you're watching their videos. After attending their classes, things clicked in my mind months or years later that I didn't realize the significance of at the time.
Both are friendly and helpful; neither is going to insist on doing anything any particular way during the class. They will explain to you a couple of times how they think you ought to be doing something and then it's up to you. They both know that there's more than one way to skin a cat in traditional archery. This open approach makes the classes fun and relaxing, but it also makes it easier for you to miss subtle concepts if they aren't being pounded into you.
The big difference between the two is that Rod teaches the dynamic release and Rick teaches the static release. The only absolute I will tell you is not to try to mix the two. There are definite advantages and disadvantages to either one, but the only thing you accomplish if you try to mix them is to do away with the advantages and emphasize the disadvantages. It took me years to really understand the differences between the two. I can't say that I really had a good grasp on that right after attending their classes. Maybe I'm just a slow learner, I don't know.
Neither teaches the pure instinctive approach. Rick comes closest, and calls his style instinctive, but does believe in using the sight picture as a reference, which some would call a deviation from the pure instinctive method. I think Rick's method is very close to Howard Hill's split vision, but he may disagree with me on that. Rod teaches gap, but doesn't push it on students. Both primarily teach form, with the aiming method being more of an afterthought, albeit a necessary one.
Both teach draw and hold, as opposed to snap shooting, although Rod's hold is more of a dynamic tension where movement never really stops, whereas Rick's is a definite stop and 2 second hold. Rod will teach snap shooters, but I think you would be wasting your time if you went to Rick's class wanting to snap shoot.
Both teach an upright stance, which of course can be varied as conditions demand. Both teach the same alignment as Terry illustrates in his form clock. I think both personally use and prefer 3 under, but will teach either 3 under or split.
Rod spends a lot of time on back tension in his class. Rick doesn't spend much time on that. Back tension is just as important in both methods, but I personally think it is a more difficult concept to master using the dynamic release, which could be why Rod spends more time on it. If you really understand what Rick is saying when he says to lock your back muscles in place at full draw, then you realize that it is impossible to come to full draw with Rick's method without engaging your back muscles. It took me a long time to understand the difference between just holding at full draw using my back muscles, i.e. "balanced pulling," and locking my back muscles in place. When I finally did understand that, it was like a light went on and my shooting dramatically improved in one day. Without understanding that concept, you're missing most of the benefit of the static release.
Rod primarily teaches form at close ranges using the blank bale. Rick's students shoot at 3D animals at 15-25 yards. Rod teaches clases of a dozen people, more or less, while Rick's classes are either one-on-one or smaller groups. Both have advantages, and while Rod's classes are larger, I never felt that I lacked personal attention. I also learned from what he was showing other students in the class. Some things, like avoiding peeking, I think are best taught at some distance from the target, as I don't have a tendency to peek when shooting at a blank bale (what is there to peek at?).
I hope this helps in understanding the difference between the two approaches, although I can't help anyone choose which is better for them personally.