Depends largely on the type of hoop and tubing of each hoop. Depending on the type of tubing 3/4 and 5/8 can be identical or they can be very different..
Both are HDPE tubing.
Yes the 3/4 OD will be more responsive than the 5/8 OD. It will have a bouncy feel to it, your breaks will have a fast bounce back.. It will be about half the size of the other tubing.
I have an HDPE 5/8" LED hoop and I actually don't like it—but not because of the tubing thickness. Because of the tubing material. Mine is a 36" diameter, so that has an impact on it to, but when I do breaks with it it's so ... squishy? It loses momentum on breaks and doesn't bounce back at all. It absorbs the bounce and just dies. I just got new polypro LEDs in the same size and they're much easier to break with. I still like the HPDE one—it's pretty—I just use it for more on-body/body rocking.