Over the past dozen years or so of traveling to and in Belize, I've taken both boat and plane to San Pedro many times. I've enjoyed most trips by either form of transport.
On a nice sunny day, I really enjoy the boat ride. It takes maybe 1 1/4 hours and usually there's a brief stop at Caye Caulker, so you get an idea of what that's like (though there is no time to get out and walk around).
But, if the weather is rainy or the water is choppy, it's not all that pleasant a trip.
Fare by boat is US$12.50 one-way to San Pedro plus the taxi fare to the marine terminal or wherever your boat is leaving from, which is US$17.50 (for the taxi, not per person.)
All in all I think most visitors are probably better off taking a plane. There are two options: fly from the international airport, which is easier but more expensive (a little under US$50 one-way), or from muncipal (about US$25 one-way), but again you have the transfer by taxi, US$17.50, and a little more hassle.
I'm the kind of traveler who likes to see a lot and to do different kinds of things, and the boat gives you a chance to do that and even see a little of Belize City (which is not as bad as some would tell you). But, again, for most visitors who just spent many hours at airports and on planes, all they want is to get to the final destination and relax, and for that the easiest is just to walk a few feet in the international airport and hop a Tropic or Maya Island flight.