We've sailed the Grand Princess twice, once in a mini suite, once in a suite. We've also sailed on the Radiance in a Cat. C, or Junior Suite as they are now calling them. Below is my opinion, and could be totally different for someone else. It is very hard to beat the beauty, elegance and atmosphere of the Radiance Class ships.
There's a big difference in cabins on these two ships! The minis with Princess are REALLY narrow. The Cat. C's with RCI are really wide and spacious. I feel a bit cramped in the minis because of the narrowness. Both cabins bathrooms are almost identical, with RCI's being just a bit nicer looking. I like the TV set-up with Princess and the exposed balconies on the Dolphin Deck.
RCI and Princess are similar, but here's the difference that we see:
RCI is more young and more active. It's a fun, upbeat atmosphere with the crew being top notch. They are enthusiastic and this is apparent all over the ship. Their ships are the most beautiful things afloat. (again, my opinion).
Princess has a quiet, intimate atmosphere with a lot of couples. No one cares what you're wearing on the beach, what you're doing and no one seems to be trying to impress anyone else.
Give it a try, if you don't like it, go back to RCI. I think everyone should try as many different ships and cruise lines as possible to help them determine what suits them the best.