As a soldier in a fairly gruesome time in history, Jasper had to have an easier time than most with the idea of killing for the sake of one's own survival (not to say he was a murderer or evil in life at all, just that when "kill that person or die yourself" is a regular issue for you, it becomes easier to kill). Then he became a vampire, and the same thing continued, but with more ease and drive. His ability to kill carried into his vampire days for so long until he became "vegetarian". It's more than just fighting the vampire side of him, it's fighting the human Jasper side as well.
SM said that Bella had such as easy time not because of her shielding gift, but because she knew going into the transformation that human blood wasn't going to be an option - she is the only vampire to choose to be a vampire, and choose to be a "vegetarian" along with it - the vegetarian vampires that exist already didn't choose to be vampires, and the other vampires didn't choose vegetarianism.
Watching someone else have a very easy time doing something you know is the right thing to do, but that you struggle with regularly is torture (ask any woman who's gone on a diet with her husband when he loses weight twice as fast as she does.)