There are more differences than you think. The width and offset of any wheel will determine the width of the tire that one coud run.
Most common differences:
16" tires do cost more, but the load ratings are higher; and with the more plies, the longer the tire will last.
16" wheels do handle so much better on the street then the exact 15" counterpart. If you take the exact same tire and wheel package but make one a 15" wheel and one a 16" wheel, then run them on the same rig you will tell a night and day difference. The 16s track straight and true, do not follow ruts as bad, ride better, and handle better as well. The sidewall on a 16 will be 1/2" shorter so technically there is a possibility of more rim damage off-road as some would argue (I'm running 17s on an off-roader). I've ran everything from a stock wheel to aftermarket 15", 16" and 17" wheels.