I thought shows were great on both lines, but I give the edge to Princess. When we were on Diamond Princess, both the shows AND the sets were amazing. I recall remarking that I had never seen such elaborate sets in a ship's theatre before. And, the quality of the shows matched them -- superb choreography, music, theme, dancing, and singing. Of course, Carnival didn't do a bad job either -- it was still excellent, just not as superb.
There are also a few differences in the timing of the shows between the two lines. As you know from being a past guest, Carnival runs the Welcome Aboard show and the Legends show just one time each. (And, as a past guest, you know why -- but I'm not telling.
). On Princess, shows are held twice -- and, the two major production shows are each held three times (two on one night, one on another). This is so that those with Anytime Dining can have a chance to see the show, but all pax can go to as many shows as they wish as many times as they wish.