I haven't had a non-reflex 500 mm lens, but the problem is about the aperture being fixed: I can't change the aperture value, viewfinder is signifficantly darker than even f/5.6, I can't use a split-screen focusing and as a result, I often focus in the wrong place and since DOF is shallow, my subject ends up out of focus.
DOF is the same as with plain refractive lenses.
Dimness of viewfinder is basically the same as with a refrective lens, as I assume one does not consider a lens of 5.6 or faster. The front mirror though will reduce the effective speed of a catadioptric lens. On the other hand the entrance angle of light is decisive for a viewfinder and here one likely compares apple to oranges as optical design at both types vary.
The lack of incorporated further apertures is rather theoretic as in practice one would use these lenses of both types rather open. (Unless on heavy tripod and static subject.)
The main advantage of catadioptric lenses is their compactness, though there is much difference between early and late designs.