I've read in a number of places that Pike at some point in the past has betrayed Thornton.. can anyone shed some light on when this was, and why?
I think it's very important because it helps us understand Thornton's justification for now hunting down his former allies, as well as Pike's regret that later informs the powerful ending.
I don't think he intentionally betrayed Thornton. Pike felt guilty for getting away at the time Thornton got captured. There was a knock on the door when the two were in a hotel room celebrating with a bunch of ladies. Thornton when he hears the knock, is cautious and says something like "hold it", right before one of the ladies is about to open the door. Then Pike says, "relax, it's just some champagne we ordered." The door is opened and the first man through shoots Thornton, who is nearest the door, in the shoulder. Pike runs into an adjoining room, while the shot intended for him ends up missing. We hear glass breaking, indicating he went out through a window. One of the LEOs asks "did ya get him?"
To which the other replied, "no, the son of a bitch got away." They probably could have pursued Pike at that point but seemed content to have at least gotten Thornton, and decided not to. I think Pike carried some guilt because his lack of caution when they hear the knock on the door, led to Thornton's capture.