124gr HST is fine, so long as it's reliable in your gun and you can shoot it well.
But to answer your question, as a general rule (there are always exceptions) heavier bullets will penetrate deeper than lighter bullets within a given caliber, and penetration is generally accepted as the most important parameter when it comes to bullet effectiveness, after shot placement. However, it's usually only the lightest bullets in a given caliber that tend to lack sufficient penetration. In 9mm, 115gr and lighter tend to have shallower penetration (rounds using the Barnes all-copper 115gr HP seem to be the exception).
My own personal preference, based on research I've done, is for medium-to-heavy HP loads for SD, whether standard pressure or +P. I use 147gr HST, but 124gr HST is good-to-go if that's what you have and are comfortable with it. I see no reason for you to change unless you just want to try something different.
FWIW, the 147gr HST I use in my Beretta 92FS has never malfunctioned, even when I attempted to induce a limp-wrist failure.