The issue is trust.
In order to trust my life to a model, I have to have
(a) faith in the model
(b) faith in the implementation
About models
If we talk about models, my thinking has changed over the years as the results of research come in. In the late 90's and early 2000's a lot of divers were on the deep stop band wagon. RGBM became popular and several ascent strategies based upon slower deeper ascents sounded appealing. The logic of controlling bubbles seemed sound and the promise of RGBM to redistribute time from shallow to deep, therefore getting the diver out of the water sooner, seemed to offer promise.
At the same time WKPP were bending divers on a regular basis using these kinds of ascent strategies, in their case with ratio deco, and I started taking a more conservative approach. I started putting in the deep stops suggested by VPM (I was using VPM, not RGBM but its internal workings are based upon similar principles) and the shallow stops suggested by Buhlmann, which is the model my computer was using. It seemed like a reasonable thing to do at the time.... a sort of fence sitting.
Then Mark Ellyatt just about killed himself using RGBM in 2004 (I think) and my thinking changed again. I spoke to Mark at length about that dive and his thoughts about the current deco models and came away from that convinced that RGBM could only be used on fairly benign technical dives. Mark also told me that at the time ALL of the deep divers had gone back to using Buhlmann. He also said to me that even Buhlmann needed significant "padding" for really deep dives and that more research was needed to calibrate it for use at depths deeper than 100m.
My conclusion was that there are no "perfect" models but of the imperfect ones, Buhlmann seemed like the wiser choice. So after 2004 I went back to using Buhlmann again but slowed my ascent from 21m to my first required stop to 3m/min. That seemed like a reasonable thing to do. I've been doing that ever since, so far (knock on wood) with good results. At the same time I NOW think this procedure needs reassessment but I haven't taken time as of yet to talk to my diving partners at length about it.
Then in ... 2007? NEDU started doing very interesting research and by 2011 it was clear that the bubble models were essentially "broken". I felt vindicated in my faith in Buhlmann as some of my friends were still using RGBM or gradients that made Buhlmann work like RGBM. Since 2011 I have become convinced that the bubble models are unsuitable for technical diving and my faith is now squarely on Buhlmann again. Back to square one. At this point I was still doing my last stop at 6m with (knock on wood) good results. Given the most recent discussions and the advent of heat maps for visualizing dives, I now believe that this procedure needs reassessment too.
So basically where it comes to trust, I "trust" Buhlmann more than any other model, even though I know it isn't perfect, and I try to base my procedures upon not pushing the boundaries of that model.
About Implementation
If we talk about implementation there are two main factors for me.
1) can I trust that the model was programmed professionally and correctly?
2) can I trust that the company takes innovation seriously?
On #1 I tend to want to know that the programmers working on the project are good. In that sense "open source" implementations appeal to me because there are no secrets and there are some very good programmers working on these projects. I know this isn't always feasible so a company with a strong history of problem free implementations is a good second bet. Everyone can name the main players in the market right now so I don't need to do that here but what I'm saying is that I would choose one of those before I chose for a computer made by a Chinese toy store and coded in a "code factory" in India.
On #2 what I find important is to know that the programmers and/or companies are up to speed on the most recent research and have the best interests of divers in mind as their programs evolve. In a recent discussion, I said that I am no longer using Vplanner or Multideco and it is for this reason. I'm reasonably certain that the programs are correctly implemented but I am also sure that the people involved have no interest in further development of those products beyond the paradigm that was popular in 2000. In fact, in recent discussions it has become clear that they not only fail to innovate but zealously resist innovation. That's a red-flag to me.
I would, therefore chose for an implementation that evolves over time as our understanding of deco theory evolves over time. For example, Suunto, despite the horrible decision they made to embrace RGBM, is such a company that takes innovation seriously and stays abreast of current deco research. I'm sure that most of the big players among computer manufacturers do the same. Seeing that a company does this is good for my confidence. Good for trust.
R..
