In point of fact, revolvers are, by design...MORE complicated, at least in the mechanical sense. All one needs to do is look at the inner workings of a revolver versus a semi-auto to realize the truth of this. Even without doing that, just thinking about what functions the revolver must perform, mechanically, with every trigger pull will tell you which is more complicated. With the semi-auto, upon pulling the trigger the hammer (striker) is drawn fully back (in a DA pistol), the sear is tripped, and the hammer propelled forward to strike the firing pin. In a revolver all of the above must occur, plus the additional complexity of unlocking & rotating the cylinder, stopping and locking it in the proper position, and ideally this will occur before the hammer has fallen.
However, this doesn't necessarily change the dynamic of the discussion. Because of the myriad other factors which can cause a semi-auto to have an issue (something impeding the movement of the slide, limp-wristing, weak ammo, HP or other unusual shape which may fail to feed) the revolver will, generally speaking, see more rounds between mean failures. BUT...this in-and-of-itself does not tell the whole story. Most malfunctions that are experienced by semi-autos can be corrected in as little as 1 or 2 seconds, while a revolver malfunction, rare though it may be, will quite often take literal minutes and sometimes the application of a great deal of brute force to correct.
I have experienced, and witnessed, several malfunctions with new and used (but well-maintained and completely serviceable) revolvers. In every case, said revolver was out of action for several minutes, at a minimum. I have also experienced, and witnessed, many more malfunctions with semi-autos, all of which were capable of being corrected within mere seconds.
Overall, I believe the difference in reliability between the two platforms balances out. The revolver will see less malfunctions overall per "X" number of rounds...while the semi-autos greater number of malfunctions will also be much more quickly corrected. My thinking is, with decent training, I know I can quickly resolve most semi-auto malfunctions that come my way...if I'm unlucky enough to experience a malfunction with a revolver, it's unlikely that any amount of training will enable me to "quickly" resolve that issue. Once, during a match, my semi-auto (which was my carry gun) decided to develop extractor issues. During one particular course of fire I experienced some 8 failures to extract while firing approx. 30 rounds. Because of malfunction clearance drills, I was able to respond almost automatically, and complete the course with a less-than-horrific score...not the worst that day, not actually TOO terrible, all things considered.
Having said all that...I currently carry a semi-auto as my main carry gun (Glock 32) and a revolver in my pocket as a BUG (S&W 642).
Tim