Murder rates are often used as proxies for crime rates in international and cross-temporal comparisons because murder definition/reporting is consistent. Other crimes like rape (definition creep) or theft (goes unreported if not likely to be punished) don't have this property.
However, medical advances (both in terms of technique and access) have a massive effect on murder rate. Injuries that would kill someone in 1950 are usually treatable today, with huge improvement since the Vietnam war. The gap with pre ~WW2 (before antibiotics!) is even larger. 
Note that "improved medical care" doesn't just cover medical tech; transportation and communication improvements are also very important. Getting to the hospital fast leads to massive difference in survival rates. Presumably ubiquitous cell phones make this even quicker today.
To put concrete numbers on it: if aggravated assaults had been as lethal in 1999 as they were in 1960, there would have been 3.4 times as many homicides as there actually were.
This applies much more strongly across longer time periods. The tech difference between the present and 1900 (no antibiotics, few motor vehicles, few + immobile telephones), let alone the Middle Ages (no germ theory or understanding of hygiene) is vastly larger then 1960 vs 1999.
Why does this matter? The major costs of crime on quality of life are not from murder, because murder is rare and highly concentrated among a few demographics (black men in the US, but it varies by country). They are from much more common crimes like assault, mugging, burglary...
...rape, and so on, as well as general public disorder, such as vandalism. Murder is a reasonably good proxy for these things because all crime and disorder tends to go together. But the ratio of murder : crime + general disorder declines over time.
This means that graphs like this, which generally show homicide rates not too dissimilar to mid-century lows and far lower then medieval estimates, massively, massively understate the actual relative prevalence and impact of crime compared to the past.
As a rule of thumb, if comparing present homicide rates to the mid-20th century, you should probably multiply by around 4 (to account for an extra quarter century of progress since the 3.4 estimate).
If comparing to the early 20th century (no antibiotics, comparatively terrible communications and transportation), the number will be higher. I suspect the gap between the present and medieval Europe is probably around an order of magnitude or even more.
True crime differences with the recent past are probably closer to the below graph (with the earliest parts being underestimates due to high standards for what constitutes a crime, and the later portions being underestimates because higher rates=> less reporting of minor crimes).
In particular, mid-20th century Western Europe (including Britain) had near-0 crime, probably lower then Japan today. For instance, in the 50s, the British homicide rate was around 0.7/100,000. This is with a young and booming population and 50s tech, unlike modern Japan.
When you see comparisons like "inner city America has medieval murder rates," keep in mind that that accompanies vastly greater non-murder crime and disorder.
Source (available on sci-hub if you don't have access): journals.sagepub.com/doi/abs/10.117…
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