I’ve heard it said that medieval society was a lot more violent than the modern day, not just on a geopolitical level, but all the way down to the level of street violence. Is that true?

There’s a whole scholarly debate about this, in part because we don’t have anything close to minimally decent statistics from that period, so it all comes down to these academic bank shots where you’re looking at court records or burial records in a given area and then everyone argues about how representative the samples are. 

Steven Pinker and those who agree with him argue that murder rates were way higher in premodern levels, there are plenty of people who disagree.

Personally, I’m unsure. On the one hand, premodern societies had much weaker police and judicial systems, so potentially there was less disinhibition for just hauling off and killing someone who pisses you off. On the other hand, various technological advances (the invention of the gun, the invention of modern industrial poisons) makes killing people way easier than the messy business of having to do it by hand, and rising urbanization means people are bumping into strangers more often who they might want to kill and makes it easier to disappear them or vanish yourself.