They're both excellent places, both well run and offering good value for the money.
For me it would probably come down to two things: Price and what you're looking for in terms of location.
In location, Banana Beach is about 1 1/2 miles south of town. That has pluses and minuses -- it's a little quieter, the beach is better, but getting back and forth to town regularly does require a golf cart or a taxi. The Palms is handy for those who like to pop out for a quick bite or drink anytime day or night, but the location at the edge of town means that there's a lot more traffic on the water and also foot traffic up and down the beach.
On price, Bananas typically is a little less than the Palms, but it really depends on the specific deal you get.
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