ls would seem to have longer throw, gsr shorter, and type r is even shorter. that's because they have different gear ratios. shift stem itself is the same. get poly bushings for the shift linkage, and be done with it. most aftermarket short throw shifter do make the throw shorter, but have a very notchy feel to 'em and some do tend to grind the gears
i tend to stay away from short throw shifter. stock with poly bushings = best