I was never trained on the GUE version of Ratio Deco, but I was thoroughly versed in the UTD version. I took half of a Webinar conducted by Andrew, I took the full class from Andrew in person (although he never sent the card), and I used it for all decompression dives for several years. Because I had some questions and concerns about the overall concept, I asked a lot of challenging questions. I then had a very detailed email exchange with Jarrod Jablonski of GUE about the topic. I believe there are mathematical differences between the two, but to me the main difference is in the approach to using it, and I think I can explain the reason Aquavelvet referred to it as religious dogma. I will try to compare the two in several ways below. It has been several years since I left UTD, so this might not reflect changes that have taken place since then. If there have been changes, I will happily be corrected.
My first true encounter with the UTD version was in the webinar conducted by Andrew, and one of the students asked about some of the research behind it. She wanted to know how she could be sure it worked. Andrew replied that you had to have faith, meaning you had to have faith in him when he said it works. She was incredulous and made a comment about doing something like that with nothing but faith as an assurance that it worked. In comparison, Jarrod Jablonski explained how the mathematical construct enabled you to create a profile that closely approximated an established decompression theory that had been tested. IN other words, your assurance is that you are recreating very closely an established and tested protocol. In that Webinar, Andrew never mentioned its relationship to any established program.
As Jarrod explained, the GUE version is supposed to approximate closely an established protocol. Jarrod told me that if it departs too far from the established profile, then it is wrong. Students in class are supposed to be able to show that their results are close to that established protocol. When I took the full UTD class, whenever we worked out a profile in Ratio Deco, another instructor worked it out using an established program for comparison. In each case, the differences were celebrated as clear evidence that Ratio Deco was superior to the established programs. Because Ratio Deco is assumed to be correct, any differences showed the defects of the other programs.
According to Jarrod, Ratio Deco only works within a certain range of parameters. Get outside of that range, and it starts to depart too far from the established program on which it is based. According to UTD, UTD's version of Ratio Deco works for all decompression diving.
According to Jarrod, Ratio Deco was created at sea level and has never been tested or recalculated for altitude. He said common sense would tell you that it would have to be adjusted for use at altitude. According to UTD, diving at any altitude does not make enough difference to merit any changes in Ratio Deco. Since I did almost all of my decompression diving at altitude then, I asked Andrew how he knew that. He said that he sometimes dives at Lake Tahoe, and he's just fine using it there as is. Being very concerned with the altitude issue, I pushed it, and I was told that no one has ever been bent at altitude using Ratio Deco. I can name 5 myself. Well, it is true that they were bent, and it was true that they were at altitude, and it was true they were using Ratio Deco, but there was another reason for them being bent. It was not due to Ratio Deco. So what was that other reason? Well, we don't know, but we know it was not because of Ratio Deco. How do you know? Because altitude is not a factor in ratio Deco, so it could not have been the cause.
At that point, I was still using ratio Deco while diving at altitude, and I was still concerned. I made the mistake of writing on ScubaBoard that I was concerned about whether Ratio Deco had to be adjusted for altitude because I knew a couple of people who got bent while using it. That was just about all I wrote. I was contacted by a UTD representative and told that if I wrote anything like that again, I would be reported to PADI for my unprofessional conduct in demeaning another agency. When I asked what I had said that was wrong, they said that after I mentioned that they had been bent, I should have gone on to explain in detail why it had nothing to do with altitude. (I guess I am risking that report right now.) That was pretty much the end of my relationship with UTD.