Easy, really. I like the breezes. The east side is also very pretty in my opinion. I don't know about the west side but we always see frigate birds and pelicans as we walk up the beach. Especially if someone is cleaning fish.
I also prefer sunrises to sunsets. I'm willing to get up to see them and may get otherwise occupied at sunset time.
Basically, though, I want the breezes. It can get really hot on Caye Caulker in February and I think the breezes help.
CC's a neat place. You'll probably enjoy it from either side. Just remember that there's a reason most of the hotels, guest houses, etc are on the east side.
If you didn't, take a look at some of our pictures and you can see a good bit of the east side of the island. Less of the west, though.