Over the time I've worked as a firearms instructor and armorer, the things I've come to look for in ammunition have become increasingly simplified.
I want it to have been made by one of the major American ammunition companies, and preferably, one of those who have acquired years of successful experience in providing duty/service ammunition to LE/Gov agencies.
Ideally, it ought to use one of the more modern hollowpoint bullet designs that have been exhaustively tested to meet a range of the performance standards commonly being requested for LE/Gov use.
If one of those aren't available at any particular time, though, I'm not uncomfortable falling back on some of the old-style hollowpoint loads that have seen service for many years. Given my druthers, I just like the more modern designed bullets that have exhibited the potential to be able to more consistently & robustly expand across a range of conditions & circumstances. (I'm not a big enthusiast of "Bonded" pistol ammunition, but then I've often observed that the non-LE firearms enthusiast often seems to be more interested in such things than the broad range of other firearms instructors I've had the chance to meet over the years.
)
Whatever brand/load is chosen, then it needs to demonstrate that it can reliably & consistently feed, chamber, fire, extract & eject from
my pistols, or any issued pistols I might be using from time to time.
Muzzle velocity & energy? As long as it falls within the normal range expected for whatever caliber/load is involved, meaning QC by the manufacturer, I don't really look at the numbers or use them for comparison purpose. They just need to run within the stated/specified velocity window (which is pretty important when it comes to helping provide for optimal, reliable functioning in semiauto pistols).
"Stopping Power"? Sorry, but unless we're talking about disc brakes in motor vehicles, I don't pay much attention to the term ...
Just my thoughts.