I can compare drivers running red lights to cyclists running red lights based on my experience. I don't believe there's any hard data on this.
From what I can tell, drivers tend to run red lights either because the light just changed and they couldn't stop in time or because they're distracted. In contrast, cyclists who run red lights tend to wait for traffic to clear. I didn't realize the difference until I tried talking to cyclists who run red lights (not recommended by the way; they tend to be jerks). So in that sense the two are not comparable.
Plus, as bikes tend to weigh less and travel less fast than cars, the potential for harm for a cyclist running a red light is greatly reduced compared against a driver running a red light.
Here are some helmet cam videos that I took that show red light running drivers:
https://www.youtube.com/watch?v=TTv_3D-1ehA
https://www.youtube.com/watch?v=JispW0pTQGA
After the first video, I saw that the driver stopped nearby, so I went to speak with them. They admitted they were distracted. I have no idea what happened in the second video. If I were not paying attention in both cases I would not be writing this post now. In contrast, if a cyclist did the same then I'd probably be here.
That's not to say that all cyclists who run red lights look carefully. Here's a helmet cam video that I took which shows a cyclist brazenly running a red light in a way that I think is particularly dangerous:
https://www.youtube.com/watch?v=mHRA4060C-k
And here's a more recent video of mine showing a Bird scooter rider running a red light:
https://drive.google.com/open?id=19Bl1ZhMvxbLliIyNkNe_Aj3QWD...
(Apologies for the language.)
This last one was probably the most dangerous time someone ran a red light that I've personally seen. I was wearing a high-viz jacket at the time and find it hard to believe they would not see me if they looked. They might have been blinded by the sun.
As for speeding being safer, sure, that's true sometimes, but what's the net effect? Just focusing on the good isn't representative.
I also sometimes see people bring the time saved from speeding into consideration, but in my experience speeding doesn't save much time unless you're on the highway. If you're in a more densely populated area with traffic lights, your speed is more limited by the traffic lights than anything else. I know this as a cyclist because it's not uncommon for me to see the same people at each light during my commute. The effective traffic speed is doable for a cyclist. Speeding won't get you there faster.