I agree that it depends upon the ship and your budget. We've sailed both with the kids, only CCL alone.
Spring break, the kids had the choice of the Glory (carnival) or the Mariner (RCI) leaving same port. Daughter wanted nassau for purse shopping initially. They chose the mariner because of the rock climbing wall, ice rink, putt-putt, in-line skating, johnny rockets and kids club, with the teen deck area.
Now mind you, these two kids have happily sailed CCL two times before. We paid $235 more per person... to give them their choice, no nassau shopping..
BUT this is what appeals to the kids! Rob and I see NO difference in adult amenities to justify the added cost and we sail CCL to save $$ and sail twice a year.
Food and service varries with each ship, RCCL is decorated more subdued and classy, but we have more nightlife fun on Carnival... not raunchy college partying... just a cold drink, music, dancing and chatting with others till the wee hours.
So I think the LINE is irrelevant... choose a ship that meets your personality... read plenty of reviews and then decide. Both lines are great IMHO
Carol