Join Date: Feb 2010
Location: Loudoun County, VA
After careful deliberation, this is my real answer.
The obedience of the horse is in direct relation to their trainer, not the job that's being asked. Any horse can be obedient if the trainer takes the time and effort to make sure the horse understand that is required. Of course there are always variables in the equation, such as the horse being physically unable to perform. Some horses can be more difficult that others, but I believe that is more of a case by case basis, not a genre of riding. I won't go on and on about that though, since this thread isn't about what makes up great trainers.
Another thing to note- certain breeds of horses are more suited to certain sports. For example, the reason for obedient horses in western pleasure could be that a lot of them are quarter horses, which for the most part are a calmer breed.