Relative to the performance of the tucson, nothing much other than the size of the hitch opening, 1.25" vs 2". If you already have accessories for 1.25" like bike racks, then a 1.25" is worth considering. However, if you don't own any accessories yet, then I'd get the 2" class III hitch because it's bigger, more stable with racks, and can hold more tongue weight.