IMO JFET and MOSFET drives are usually overdrives as they clean up really nicely and sound warmer, smoother, rounder AKA 'tube-like'. However, they tend to mush up under higher gain. IC drives tend to be edgy and don't clean up as well as FET drives, but they can usually take more gain and maintain clarity, 'hifi-ness', hence they are pushed as 'distortions'.
Of course, you have to factor in the circuit, amp, pickup output among many other things. There are also many exceptions so this is all IMO. That all being said, I think both types have their places on any pedalboard.