Hawaii and Caribbean diving are slightly different animals. Hawaii doesn't have big colorful sponges or sea fans and such, but it does have nice hard corals. You'll primarily see about 7 species of hard corals. The Big Island has more healthy live coral reef than the other Hawaiian islands
NOAA - National Oceanic and Atmospheric Administration - New NOAA Maps Show Big Island Has Most Live Coral of Main Hawaiian Islands and depending on the spot you can be wowed or disappointed in the coral structure in comparison to what you've probably already seen.
Hawaii doesn't generally offer big shoals of fish, but it has several hundred species, 25-30% of which are not found anywhere else in the world. You'll regularly see about 20 some odd species of butterflyfish, 20 some odd species of surgeonfish/tangs, about 10 species of triggerfish, and 40 some odd species of wrasses, as well as lots of other types of fish. We get some people who are really into the fish and are used to diving the Caribbean and just love the variety we have here. We have little in the way of "big" fish other than the mantas and the occasional shark or jack. Hawaii is a geologically young island chain so we're not loaded with apex predators. We do have a small grouper (call it 18-20 inches) that was introduced back in the 50's and is now a pest.
The Big Island is interesting for diving because nearly every site offers deep water dropoffs and shallow reef, so you can get a lot of variety on any single dive. There really is no "season" when it comes to spotting fish, the fish are here all of the time. Spring and early fall do seem to be a particularly good time for juveniles of many of the species, but other than that you're not really likely to notice any major differences in fish populations from one time of year to another.
I hope this helps. Hawaii diving can be real interesting if you're into looking for new oddities you haven't seen yet.
Aloha,