Half Moon Cay is wonderful -- if you like a day at the beach! That is what it is, a great beach and pretty much nothing else.
Being from California, it is not much of an attraction for us. If you are from Ohio or Minnesota it is probably a slice of Heaven ..
Cozumel is a tourist port par excellance. There are many many touristy things to do there, from beaches to swimming with the dolphins to sitting in a bar, and of course shopping shopping shopping. If a bustling tourist port is your thing, you will like it there.
As always, it depends on what YOU are looking for in a cruise.