The two places are quite different, in location, amenities, style of management ... and price (especially off-season).
Mayan Princess is a pink three-story building in the heart of "downtown," on the water but in the midst of things. It doesn't have a pool. The units are attractive though not deluxe. I've enjoyed staying there. The management is casual but competent and friendly. Especially off-season, it's usually a real value, though I don't know what off-season rates will be this year.
The Belize Yacht Club is a quarter mile or so south of town. It's on the water, but there's a seawall rather than a beach. Beautiful pool. The BYC has gone through a lot of changes -- condo, timeshare, now the emphasis seems to be more on the hotel side, and there's a meeting facilities for groups. The units are attractive, at least the ones I've seen, either first or second floor. Management is usually described as so-so. Rates generally are quite a bit higher than the Mayan Princess.
Personally, I'm more comfortable at the Mayan Princess, but the BYC is a bit more upmarket I guess.
There are a number of other quality condotels on the island in a range of prices. Banana Beach is one of the best values and it offers a lot for the money. Banyan Bay is considerably pricier but it has deluxe two-bedroom units. There are several others that are very nice -- Belizean Suites, Coral Caye, The Palms being just three others.
Belize First Magazine http://www.turq.com/belizefirst/