Here the general description of the division from the USEF -
Hunters over fences are judged on performance and soundness. Judges are looking for great jumping style, quality of both looks and movement, as well as willingness, manners, and suitability of horse and rider. The round over fences itself should be judged on evenness of pace, as well as consistency of distances. In over fences classes hunters are judged over fences that simulate fences found in the hunt field such as coops, walls, gates, etc. Some hunter classes over fences are what we call Handy Hunter classes. These classes emphasize tight turns, creative approaches, brilliance and pace. Hunters are also shown on the flat. These classes are called under saddle classes and are judged both directions at the walk, trot, canter, and sometimes the hand gallop. Movement, manners, and quality are judged at all gaits."
And here's link to another thread were hunters and hunter judging are discussed at length. How are hunt seat classes judged?
And here's a link to one of the best hunters in the USEF laying down a winning trip -
If you want opinions on whether or not your horse would do well in hunter competition, it might be best to post photos or videos. Please don't feel your horse has to look, move and jump like Rumba in the link above, there are lots of different levels to hunter showing, and he was pretty much at his own level at the top.