Hunters - judging is based more on the movement and jumping style of the horse (knees tucked, well footed take offs and landings, easy and steady gaits, etc.) and how well the round goes overall. Your horse needs to be able to keep a consistent pace throughout the course (not rushing fences or hesitating). Hunter courses tend to be very straight forward.
Jumpers - judging is based on how clean and fast the horse and rider can make it around the course without any faults. Style doesn't really play a role in it but your horse needs to be very responsive, balanced, and agile. Jumper courses can get very complicated in order to challenge the horse and rider. Tight turns, different stride counts between jumps, different heights and spreads, and objectives that challenge the rider's ability to plan and execute a course are common.