We have cruised Celebrity exclusively so I can't answer your question about Royal Caribbean. I didn't mean to scare you away from Celebrity, but I don't want you to be disappointed in your vacation.
We have taken 7 day or longer cruises on Celebrity mostly during non-school vacation times. Summer vacation cruises of 7 days in the Caribbean (which Celebrity no longer does) seem to have a little more activity than winter cruises, cruises that are longer in length, or 7 day Alaska cruises. However we have taken one two day cruise on Celebrity that was strictly a party atmosphere and we felt that we had been transported to a different line. I guess everyone was trying to get their money's worth out the cruise. People were 5 and 6 deep at the bar, the disco was so packed that they couldn't admit anyone else into the lounge until somebody left.
Celebrity is a great cruise line but it has its own niche in the mass market line. If you are looking for a party type atmosphere then you will want to go with a party type ship. If you watch the commercials on TV, you can see what kind of passengers the cruise lines are trying to attract. Celebrity's ads are laid back talking about quality of service ("I was a king", "my butler served me tea every afternoon").
From the ads that I have seen lately, I can see that Carnival is trying to change their image from a total party ship to one that appeals to families (the Christmas ads featuring a wrapped up cruise ship) as well as empty nesters (the older couple enjoying a dining experience).
A good travel agent will help you find a cruise line that meets your needs. Also there is another message board where there are rollcalls and you can find meet the people who have booked the cruise you were thinking about.