We've had many sailings on both. Decide if Glacier Bay is a must. If so, do Princess. For DH and I, we enjoy the bit more elegant Princess and would choose over RCCL except for newer larger RCCL ships, which we enjoy a lot for variety and top entertainment. When adding our young adult kids, we only consider RCCL and NCL, and (oddly) Disney (which has great venues for the young 20s), and possibly Celebrity as it has a bit "hipper" vibe than Princess, in various small pocket bars and entertainment choices.
Princess as others have stated doesn't have enough "fun/young" stuff. Holidays and cruises during school breaks tend to have more kids on Princess than other times. RCCL has more kids/young adults all times.