For over a century the standard rate of twist for a 9mm barrel has been just about 1:10". This has worked just fine in a defensive handgun since George Luger designed the 9mm.
Some have worked on changing the rate of twist for 147 gr. bullets in full auto SMG's and other guns, and for precision shooting matches, but we can let that go in this discussion... maybe.
The difference between 115 gr.s and 124 is 9 grains. A grain is one 7,000 of a pound. Not enough to make a great deal of difference by itself (other than a bit in point of impact). Other factors will be more important.
First: the shooter, their experience, preferences, and how well they can shoot.
Second: the gun. It's weight, style, purpose, trigger, etc.
Third: the ammo. What type bullet, manufacturer, lot, is it standard vel? +P or +P+? That will make a difference in the shooters ability to shoot accurately from a particular gun. More recoil and more muzzle blast effects a guns shoootability for many.
Folks who argue that 124 gr. is more accurate generally mean that they favor shooting 124 gr and shoot that more accurately usually, from a particular gun.
Note here that folks do not mention whether it's +P+ 115 grain or +P124 gr. or standard velocity fodder. They make no distinction. This means that they claim to shoot all 124 gr ammo the same regardless of bullet type (ball, JHP, hard cast lead, etc.) velocity, or manufacturer. This is very unlikely. If they prefer shooting 124 gr. for one reason or another that could account for it. It's a preference for some.
tipoc