Based on my experiences on both cruise lines, it sounds like, given your ages, that Carnival might be closer to meeting your expectations. Both cruise lines have many similarities, but it does seem to me that the average age of any given Carnival passenger is younger than the run-of-the mill Royal Caribbean passenger. I am 41 and my wife is 38 and we seem to fit in pretty well on Royal Caribbean and we do seem a bit older than average on Carnival, although that has never been a problem in any way.
Both cruise lines offer nightclubs on their ships with your typical dancing, etc and both have plenty of drinking venues on board as well. The activities between the two lines are very similar and I have had just as much fun on one line as the other.
If the ages of your fellow passengers don't really matter to you, then I would suggest picking the cruise line with the ship that you like best.
The bottom line is that you really can't go wrong for this particular itinerary (the Bahamas), especially since you really don't have any frame of reference.
Again, this is just my opinion, and I'm sure some folks with disagree with me.