Jumpers - It's all Speed and no faults, you could ride all willy-nilly and as long as you don't knock anything down and don't have speed faults you'll do well.
Hunters - It's judged on the horse, you can still ride willy-nilly, but you're horse has to have the correct lead, lead changes, no swaps, even pace, and jump in style.
Equitation - This is where rider form counts the most, if you ride poorly you won't place at all.
Equitation is important in all riding events because HOW you ride effects HOW your horse goes. Riding poorly will effect your horses balance and style. There are some truly amazing horses out there who are able to compensate for their rider's jumping ability, but most horses its very easy to see how poorly the rider rides, based on that horses way of going.