When someone says the meat is sweet, it's not sugary sweet in any way.
It's a very difficult thing to describe, so I think that sweet is the best that can be said. Fresh or light, or subtle would be other adjectives to use, but thwy also cannot describe it well.
For instance, try to describe a piece of high quality tuna sashimi.
Also, just an FYI, stone crab season just ended in Florida. It goes from mid October to mid May.
If you are going to make the pilgrimage, try to go in January or February. That way you can try the other of Florida's specialty seafood: spiny lobsters.