I've been there a lot and caught fish most times from shore. There's the odd bonefish in the shallows around the island but never seen any great schools, just singles and pairs. Never fished on the other side of the split but from what I've heard there's more bones over there if you're willing to go for a paddle.
Had a friend take us out to reef and caught a ton of barracuda and various reef fish, but crappy equipment and rods built for marlin takes a lot of the fun out of that.
You used to be able to basically fish from your bar stool at the split and the tarpon would come to feed under the lights at night. A lot of people try to catch them but dont' have luck with typical tarpon patterns. The only thing that ever worked for me was dead drifting small shrimp patterns in the current (the shrimp come to the lights and attract the tarpon). Actually had luck with top water rapalas as well one trip but after I hooked a couple they spooked for the night.
The best flats fishing is accessed via ambergis caye, they have the classic flats you see in the magazines with tarpon rolling and permit tailing. When I asked nobody from caye caulker was willing to make the run, i think it's pretty far.
I've also talked to guys that jumped in tour boats headed for the outer reefs, fished all day and had them pick them up on the way back in.
It used to be a real gem of an island, go slow