I have never been on Carnival, but I have been on Royal Caribbean!
Although I haven't been on Mariner of the Seas, I have been on her sister ship Voyager, and my brothers friend just came back from the Mariner! He only had good things to say about it.
If you choose the Mariner you can please both your children. There is a huge basketball court which your son would love, plus the arcade! And on Voyager they had some really fun activities, so I'm sure they will on Mariner too! Plus the pools are really nice! It is very easy to meet people on royal caribbean, when I went on it, a large majority of the teens went the first night to meet people! Plus Johnny rockets is so fun, and the ice skating rink and the rock climbing wall! You will never see your kids! lol
So I say Mariner of the Seas!
none at the moment =[
-Ocean Coral & Turquesa Resort; August 2009
-Mariner of the Seas; August 2008
-Explorer of the Seas; July 2007
-Crown Princess; July 2006
-Voyager of the Seas - July 2005
-Disney Wonder - November 2001
-Big Red Boat..not sure when