Speaking for Galveston, which has three ships, I think the main point is not just Carnival vs RCI, but also the specific ships.
First off, if you choose Carnival I would opt for the Conquest as it is much newer than the Ecstacy. Plus, it does a 7-day cruise.
However, do not overlook Voyager of the Seas. You are lucky to have an RCI megaship in your area, there isn't a single on on the whole West Coast, though that is changing next year.
Bothships are great. Conquest is about $200 cheaper per person. But if you have kids I think they will appreciate Voyager more.
I would give Carnival the nod for food and service, But RC has really fun ships with lots of onboard activities and great shows including the ice shows.
Carnival's shows are also good, but no ice show, obviously.
Carnival is a little more crowded in the public areas, but the cabins are bigger, but on RC you can get an inside cabin with a view.
Bottom line, I would take them both and then YOU decide which one you like better. Both are good values and worth a try.