I am on stock but I also want to know.
I guess part of the reason is you can't fit wider tyre (for better dry handling) on stock rim. changing to 16" rim plus lower profile tyre ( for rigid turning) to match stock rim + stock tyre diameter to avoid error in speedo meter and other ECU computation.
weight, I guess lighter will give better pickup but more bumpy. heavy rim then higher inertia thus car will not bump so much on rough surface. may be I am wrong, any pro can correct me?
Design, easier to clean, more opening for air to cool rotor or dirt/mud to stick on it. If you drop different rim from 13 floor, I guess some design will have less dent (rigid rim) than other.