I happen to enjoy both the 21st Precinct and Dragnet. Both shows are in my top 10 favorites, for sure. Dragnet lasted a lot longer than the 21st Precinct did and eventually wound up on television. To my knowledge, the 21st Precinct never made it to the screen.

Both are police shows; Dragnet was the West Coast variety, the 21st Precinct was East Coast. Dragnet was hard-hitting, (realistic but) monotone and somewhat violent. The 21st Precinct was much more realistic because you always saw yourself at the same places when you listened. The Dragnet detectives were in a different department every week. At the 21st Precinct, you were in the muster room, the Captain's office or upstairs with the detectives. Sure, you were on location too - and those locations are where Dragnet really gets beat. The 21st Precinct had many foot traffic officers on the streets of New York City and much of the time while listening to the show, that's where you were. Dragnet used no call boxes - but in almost every episode of the 21st Precinct, someone would use a call box.
Almost every crime (episode) in Dragnet is about something important. I suppose the same can be said about the 21st Precinct. However, take an episode where a little girl is missing in each. The Dragnet episode is bloody and brutal while the 21st Precinct episode is much more suspenseful and the girl winds up being found, unharmed. Yes, brutal murders do occur but in the case of the little girl, don't you "pull" for the girl to be found unharmed?
I really enjoyed the career of Jack Webb and there's something to be said about his matter-of-fact style, especially when it came to radio/TV police work. But the actors on the 21st Precinct were not at all like their robot-like counterparts; they were realistic and human. They showed emotions (other than anger) and they seemed to care for the welfare of the people involved.
This is truly a case of two very similar shows being very, very different. If you listen to both shows, drop a comment and tell me how you feel.