If you have a new gun, sometimes the lighter 115 grain will not cycle well initially because of a stiff recoil spring, especially in small guns. The 124 NATO will work better for break in if this happens.
Yes, and especially in the micro-nines.
When someone used to have trouble with their new Rohrbaugh R9 feeding, it was almost always the case that they were using cheap 115gr practice ammo. The advice was almost always to use 124gr Gold Dots, and when owners did that, the problem went away. I imagine that most Rohrbaughs now have been fired enough that they don't have that problem.
When I purchased my Kahr CM9, I used 124gr "NATO" ammunition for the first 500 or so rounds and I never had a problem with it cycling. Now it eats 115gr WWB, 115gr Federal Champion and 115gr Blazzer Brass without a hitch.
Another thing to mention is that some pistols are either built around a particular bullet weight or don't do well with a particular bullet weight. The Kimber Solo didn't cycle 115gr loadings very well and it came with statement to owners to only use quality self-defense ammunition 124gr or heavier. The Diamodback DB9 seems to do best with 115gr or lighter ammunition and comes with the following warning from the manufacturer:
Notice: Due to potential cyclical problems involving recoil energy, Diamondback Firearms does not recommend the use of any 9mm SAMMI Specification ammunition in bullet weights exceeding 124 grain.
For self-defense purposes I think the 147gr weight class generally has the best terminal ballistics.