My opinion (your mileage may vary):
The Palms: Convenient location just at the south edge of town. Very nice condo suites, both one and two bedroom (can't recall offhand if there are any three bedroom, don't think so). Small but nice pool on the back side. On the water with beach and next to Ramon's beach but it is close to town so there is more boat and people traffic. In my new guide to the island, we give it four stars.
Caribbean Villas: South of town but within walking distance. Lovely setting -- lots of trees. Nice little beach area, with a small artificial "reef" for snorkeling. No pool. No in-room TV. Nice, helpful owners and management. Downside is that perhaps the owners need to invest a little more to bring the property up to the spiffy level of the newer properties on the island. Also, prices are on the slightly high side especially off-season (they don't drop much from in-season). In San Pedro Cool we give it three and a half stars.
Coral Bay Villas. This Southwind property (they also do Belizean Shores among other things) is also within walking distance. Nice units, all one bedroom if I recall. Beach area but, again, no pool. Good prices. We rate it three stars plus.
Bottom line is that all are fine, with The Palms having the edge on amenities. If one offers a decidely lower rate, that might be your tie breaker.
Belize books and publications by Lan Sluder:
Belize First Magazine (http://www.belizefirst.com
Fodor's Belize & Guatemala Guide (new 4th edition coming this summer)
Adapter Kit: Belize (the first and only comprehensive guide to living, retiring, working and investing in Belize -- a best-seller on Amazon.com)
San Pedro Cool (the first and only visitor guide to Ambergris Caye)
Belize First Guide to Mainland Belize
UpClose Central America
Belize Book of Lists