This is a great thread. You can tell who was in LE from the responses in this thread. Those who carried guns for 8-18 hours a day for years, mostly picked K frame guns with fixed sights. Enthusiasts who do more shooting than carrying picked heavy barrel, large frame guns with adjustable sights.
I was issued the Model 13-3 3" round butt in 1986 at the FBI Academy. Ammo was .38 Special +P 158 SWCHP, manufacturer depended on contract and inventory. Stock grips and Pachmayr grip adapter. At the same time, DEA was issuing the Model 65 3" round butt, with Pachmayr Compact grips.
Older agents were issued the Model 10-5 and 10-7 4" pencil barrel, with square butt service grips that were rounded on the bottom for better concealment (NYPD did the same with their Model 10 4" HB). Those revolvers were great shooters!
For a very short time, a special run Model 10 with 2-1/2" heavy barrel and fixed sights was issued. They were not successful for a variety of reasons, and I only saw three of them in my entire career, out of hundreds of issue revolvers. The qualification course back then started with 50 yard shooting, and the short barrel was something of a handicap, since 20% of the rounds were fired at 50 yards!
After my issue 13-3 broke 3 hammer noses within a year (twice at the Academy, and once during quarterly qualification), I figured something was dimensionally off on that specimen, and turned it in and used my own guns from then on.
I carried a variety of personally owned revolvers for the next 10 years. My big gun was a 4" Model 27-2, which shot very well with the issue .357 Magnum 145 STHP and Winchester 158 JSP. This required a jacket to conceal and it was lot of iron to pack except when working alone or doing raids, arrests, etc. I used a pancake holster that covered the sides of the rear sight. With the skinny barrel it was a fairy fast draw out of the holster - for a young Agent with plenty of shoulder flexibility. Grips were difficult as the square butt service grips were not rounded, so I used Pachmayr Grippers which were thinner.
My smaller carry was Model 19 2-1/2", which was much better when trouble wasn't particularly expected. Loaded that with the issue .38 Special ammo, which reloaded easier with the short ejector rod. Stock grips with a Pachmayr grip adapter (miss those!). Used the issue style Bucheimer thumb-break high ride holster, with slotted front. It covered the rear sight well.
Backup and off-duty was either a Model 36-7, 649 or 640. I liked the 649 the best. Stock grips and a Pachmayr grip adapter. The original issue 158 SWCHP was a kicker in those guns. The later issue Federal .38 Special +P+ 147 HS shot much better.
I tried a couple of L frames - 4" 586 and a 3" 686 - and hated them. They were a slow draw from a concealment holster with the heavy barrel and full length ejector shroud profile. Not much lighter than the N frame Model 27 either. Perhaps better in a duty-rig style holster.
After 1989, my main gun was an autopistol. Started with a S&W 459, but as soon as .45 was authorized I bought a S&W 645, as it was similar in size and power to the Model 27 .35num7 Mag. Carried that 645 for quite a few years until the Glockenspiel was issued.
Retired, I carry revolvers again frequently. My favorite is the Model 10 2" round butt. Fixed sights are no handicap, the actual sight picture is good. It hits point of aim at 50 yards and inside a 6" circle prone. The no-lock current 442 is also a favorite, although it doesn't shoot as well at 50 yards.