Larry, congrats on winning a cruise! Been on the 3 and 4 nighters outta Long Beach about 6 times. Always a great cruise, and way to get my fix in for awhile and at a low cost.
I've been on the Monarch many times -- like it very much. Never been on Paradise, because it seems to run a tad more expensive but was on Ecstasy a couple times before they brought in Paradise.
I think either would be great. I like the more upscale feel of RCCL, but Art loves the free ice cream on Carnival. And, of course, Carnival far outweighs RCCL on cabin size.
Here are links to two articles I wrote that might help you out: