I've stayed at both in the same trip to the Maldives. I believe there is absolutely no comparison between the two.
Sheraton is an easy access, close to MLE resort that I didn't find to be too unique or different. There is no snorkelling at Full Moon. Additionally, there is so much land reclamation going on that flying out of MLE, Full Moon is almost attached to the airport. Ok - that's a slight exaggeration, but it's very close these days. The minus for me is that the Full Moon is on the northern departure track from the MLE airport, so it's a bit noisy.
Park Hyatt is totally secluded and among the best out there. If you can afford it, it's a much better option. It's quiet and serene with a beautiful beach and a world class house reef.
I reviewed both Park Hyatt and Sheraton Full Moon in 2012
at my trip report here
I later returned to the Park Hyatt in 2015, a review is
at my trip report here