I sat in a corner desk right on top of a major central business district intersection. Cars never ran the light, it's too busy and complex. Cyclists did reckless, stupid shit all of the time, running lights, cutting across the diagonal on the wrong side of the road, etc.
From my POV, drivers are more predictably dumb, and dangerous when they perceive low risk, for example, they run red lights in a low traffic neighborhood and are awful about a number of things. Cyclists are less consistent and perceive risk differently. Younger people who perceive themselves as invincible in particular.
End of the day, we should have better dedicated infrastructure for bicycles and other things.
I have never seen a cyclist in the UK run a red light at a complex intersection (often only running the 'quiet' side of a T-junction, or an empty junction with a 20MPH speed limit and no cars in sight). Also worth noting is that the roads in UK cities are much narrower, I would guess 40-60, and often have less lanes and often have a bike lane of some sort.
In the US (California) I have seen all the crazy stuff. People running red through traffic, people doing a U-Turn, people going the wrong way, people crossing to go the wrong way, people blowing through a red light whilst on their phone.
However for cars, the UK has more stop lights that are for cars giving way to pedestrians, i.e. there is no junction. I have sometimes seen cars run a red on these when they don't notice/care. However in the US the red lights are at junctions, and are therefore more dangerous for cars (getting T-boned) I have however seen more people run these still.