A lot of the instructors I know can teach for various agencies, and I think they basically teach the class they teach, and you choose the card you want. That was the case with my Intro class, where we went with TDI because the instructor said they were the fastest to get the cards out (and they were quick!).

There are some differences in limits at the lower levels. I think NAUI's Cave 1 class makes a great deal of sense, because it allows you thirds and one jump, which may be all a lot of people are ever going to want.

GUE is different; the GUE cave instructors, as far as I know, don't teach for any other agency. GUE doesn't break things up into three or more steps, and won't teach a zero-to-hero class, or a class for one student. GUE classes tend to be longer (five days for Cave 1) and have a mandatory prerequisite in Fundamentals. They are also very expensive, as cave classes go. But the instruction tends to be excellent and the standards are uniformly high.

I have cards from TDI, GUE and NACD, and nobody checking cards at a gate has ever cared which one I show.