At least some returning vets were allowed to purchase their sidearms, and rifles, if they so desired. And some of those "purchases" never involved Uncle Sam actually getting any money!
Lots of them were just "kept", others were "bought" from the supply sgts (who often pocketed the money and just combat lossed the guns) and some were actually bought and paid for, with all the proper paperwork.
Over the years I have met vets who retained their service arms in each of these ways, so I do know it happened.
All else being equal (and it almost never is) bigger bullets tend to work better.