Like a fixed bar, rock doesn't move to accomodate hand rotation. Rings will train the correct muscle groups, but they rotate. On rock, it's full-out pronated grip or nothing. You might as well get sport-specific here.
I gave up ring pullups a while ago. Not because of any particular difficulty, but because I found them easier than bar pullups. At CFB, we have a huge 1.5" pipe. This adds to the difficulty, and helps grip strength as well.
If I were you, I'd get a fixed bar, and get a larger diameter than you're comfortable with. Your climbing will improve!