They're personal preferences. Raiders is the classic look and the others are "mods" to that jacket. So Temple is an inch longer, Crusade has storm flap buttons and a larger collar.
Then you have to deal with which leather. Lamb would be screen accurate and most popular, but Goat has a similar look to lamb, but is a little bit more heavier and tougher. Then you have cowhide, which is basically a thick, tough jacket. Horsehide is still quite new and would probably be my next choice for a jacket as it is super tough and looks(at least in pictures) like lamb