The history of what revolvers were carried by police & sheriffs is an interesting one, and the changes reflect both the changing technology, and attitudes of the times.
In the decades surrounding 1900, city cops often carried .32s. AND a good stout stick. Cops patrolled their beats on foot, and the .32s were lighter.
Western/rural officers went on horseback, and usually carried bigger revolvers.
The change brought about by widespread ownership of automobiles brought a need for a more powerful gun, culminating in the .357 Magnum.
6" barrel gun were still very popular, but over the years the benefits of the 4" came to dominate as most officers moved to patrolling in cars.
Also back in these dark days, generally police were forbidden to use hollowpoints. Ammo was carried in belt loops, and the hollow point was considered to be "scary" to the public, by police administrators.
Same thing, essentially, with forbidding magnum ammo, along the "justification" that many officers didn't score well with magnums.
Today, attitudes are much different. Officer safety/survivability is a much higher "public" priority. Today, instead of being thought of as "evil" or a sign the officer meant to be a "killer", hollowpoints are thought of as "safety ammo", not only being more effective stopping bad guys, but safer for the public as well, being less likely to overpenetrate, or ricochet.
The other thing about 6" revolvers (and something seldom talked about today) is that last ditch, the handgun is an impact weapon. And a 6" med frame revolver comes close to the mass of a 4" large frame, giving a slight advantage when things go all the way bad.