In my experience with both men and women divers, it's more often the women who have problems with fit for rental BCDs. Rentals are virtually always "unisex" models which is really code for "male." Women are more short-waisted than men, so when the BCD is inflated on the surface, it tends to ride way up, and the bladder often rubs against the neck under the ear rather than staying down on the shoulders where it belongs. Also underwater, women in rental BCDs tend to have more issues with the tank shifting on their upper backs because women's shoulders are narrower than men's shoulders, and the "unisex" BCDs are simply too wide in the shoulder area. I've never seen a man with a serious problem with the fit of a rental BCD, assuming the size is correct.
For this reason, I recommend that if a woman has money only for either a BCD or a reg, she should buy the BCD.
For a man with that decision to make, it could go either way, but it would probably depend on what bugged him the most about the rental gear he has used in the past.