^^^^^^^^^^^^^^^^ Overall, I think, 124s (the original 9mm weight/loading) is probably a little more accurate than the average 115gr. loading, if you're talking about factory ammunition. Most 115 loads are pretty light, and can cause function issues in some pistols, too. I know that 1911 9mms function better with the heavier bullets, as they move that slide mass easier than the 115 loads do. When I bought my Springfield Range Officer, it wasn't happy with CCI 115s, they just weren't loaded hot enough to cycle that mass. Switching to 124s fixed that quickly enough.
That said, and because I'm NOT talking about factory ammo here, I just bought another 3000 Hornady HAP bullets to load in my handloads for 9mm and .38 Supers, and they shoot fine, but if you're stuck with factory ammo, I'd buy 124s. Most ammo makers have both weights available, and given the choice, I'd pick the heavier bullets.
This brings up another topic.......the Hornady HAP bullets I have bought are 125gr instead of 124gr and they are .356" diameter instead of the normal .355".
I started using them in my 38 Supers and they were more accurate than any .355" bullet I had tried in any weight
I then tried them in my 9mm's, I dont see ever going back to .355" bullets