Varies, as noted. Some depts issue all weapons, some allow anything an officer can qualify with as private purchase, others offer a choice of an issued weapon or a private purchase weapon from a list of approved models and calibers.
Ark,
Commonality of weapons and ammo was a guiding thought long before the Hollywood bank heist.
Theory was that it was easier for department armorers to work on one gun, it was easier for department firearms instructors to teach one gun, if an officer went down any other officer could immediately scoop up that gun & use it if necessary, and if one officer ran dry during en extended engagement his or her fellow officers on the scene could toss spare ammo over.
Much of that (dating way back) finally went by the wayside as height restrictions were done away with, women started to show up behind badges in larger volume, it was clearly demonstrated (with even a court case or two) that one size did not fit all, cops were not scooping up each others guns in measurable numbers, and those of us who were subject to the "ammo interchangeability" nonsense finally started getting through to police administrators by simply saying that "If the guy or gal next to me during a major shootout has already gone through all 18 rounds (revolver) or all three magazines (auto) without accomplishing much, I certainly am not going to toss away any of my remaining ammo in their direction in a protracted engagement."
I never saw any signs of a national trend come out of that. In fact, my PD showed the video of the shootout in several lineups, it was heavily discussed, and at about that time the list of optional approved private purchase guns was expanded.
The national trend that did emerge was the patrol rifle in more cruisers.
Denis