They are close but the edge still goes to Carnival. But when we were on the Mariner, you would have been hard pressed to be able to tell the difference based totally on the activity.
It probably depends a bunch on the actual ship you pick. There are ships on both lines that are a little more sedate.
Carnival Cruise Lines:
Fantasy 90, Celebration 95, Victory 05, Conquest 05, Spirit 6/06, Freedom 6/08, Holiday 7/08, Victory 6/09, Valor 9/09, Dream 6/10, Splendor 8/10,Conquest 8/11,Magic 11/11,Triumph 4/12,Spirit 7/12,Freedom 11/12, Triumph 2/13 - The fire cruise
NCL Dream October 2006, RCCL Mariner OTS June 2007