I think there is little question that the 22 Mag is a better caliber for self defense if you choose to carry a gun in that caliber. For me, the discussion really goes to two guns as is often the case: one for range, plinking, and fun; and one for self defense. The Single Six or the like gives you both, but other than walking around the woods or in your home, I can't see using that platform for self defense. Nothing is impossible. But a smaller gun is much more useful for personal defense if for no other reason than you are more likely to actually carry it (often).
I don't believe that if you choose a rimfire for personal defense that you automatically go for the 22 WMR. But again, I think the 22 Mag is clearly more powerful than the 22LR from any platform when comparing apples to apples.
When I first started out being interested in such things, I chose a 22LR for my general defense gun simply because I shot it better than 357/38spl and the 22LR was my first handgun. I had a Colt Python then, but opted not to use it for defensive purposes unless it just happened to be handy until later in my defensive thinking evolution. I think the odds of needing a gun for self defense are over blown, but it depends on where you live and where your travels take you routinely. But it is the unpredictable event that gets you. For that reason, I carry a airweight J-frame 38spl. But I personally have little hesitation to carry either a 22 Mag or 22LR in a small platform such as the Ruger LCR.
The point about cartridge size also applies. It is much easier to load a larger caliber than 22LR in a revolver. Add in cold hands or fear, and the larger cartridge clearly has an advantage.