This debate has been going on since the beginning of time, and most likely it will still be going on at the end of time. That said, here are some observations:
1. Nothing in this world is perfectly safe or perfectlly reliable. Once you've decided to leave the house you've decided (at least implicitly) to accept some level of risk. So the real question is along the lines of: What are the practical comparative risks of unavailability when needed of a pistol vs. a revolver?
2. Empirically, a revolver will be more reliable than a pistol, for two reasons. First, the sequence successfully to fire two rounds out of a pistol is far more complicated, which means that there are more failure modes, which means that the combined probability that ANY of the modes will occur is higher. Second, the pistol, unlike the revolver, is dependent upon the ammunition in order to cycle, thus adding an entire class of failure modes that revolvers do not experience. Note that the probability that a locked and cocked pistol will fire the first round is much higher than that it will fire the second round, so if one round will do, the reliability of a pistol and a revolver probably converge.
3. In general, pistols require more frequency maintenance and surveillance than revolvers. In the scenario where you load, carry for a year, and then fire once, the reliability of the pistol varies (generally decays) over the carry time because of the migration of lube, the incursion of dust, dirt and debris, and the like, while the reliability of the revolver stays constant. At the same time, the reliability of the pistol that gets regularly fired (and, therefore, regularly cleaned, inspected and lubed) is higher than the reliability of the pistol that is "carried forever, shot once."
4. I once personally observed a very impressive demonstration. A Model 10 (and old, ratty one) was loaded and dropped into a five gallon plastic pail of mud. It was then put away for a month. After that, the pail was inverted; the mud, which had solidified, was prised out and whacked with a hammer to break it up, and the revolver recovered. Without doing anything to it, the revolver was pointed down range and fired. All six rounds went off. While I never saw the same test performed with an auto, I have no doubt that the most you'd get off would be the first round, and even that may be doubted.
5. On the other hand, what does this test tell you? Well, it tells you that if you're going to put your handgun in long term storage in mud, you should probably have a revolver. On the other hand, if you take your carry gun out of the holster religiously every week, cycle out the rounds and clean, inspect it and lube it, and then reload it with fresh factory rounds, this test tells you a lot less.
5A. Then from time to time you'll hear someone say, "Well, I've fired upteen zillion rounds out of my Suchandsuch auto, and only had two failures to go into battery." What does that tell you? Well, it tells you that his Suchandsuch, maintained the way he maintains it, is pretty reliable when engaged in sustained firing and maintenance. It tells you far less about how well a Suchandsuch performs as a carry forever, shoot once defensive device.
6. So the bottom line is that the question (which is more reliable: pistol or revolver) is not only difficut (if not impossible) to answer, it is also difficult (if not impossible) even to define the question. More to the point, "reliability" in strictly scientific, statistically definable terms, is probably irrelevant. The better question, as originally posed in this thread, is whether a qualified expert would trust his life on firearm X.
7. For what it may be worth, I have two handguns that, together, probably account for way over 90% of my carry. One is a stainless S&W revolver; the other is a SIG auto. I am qualified to work on both and I take good care of my guns (all of them), and both of these handguns are fired on a regular basis. Would I trust my life on either of them. Yup.