Has anyone ever ran a study on the effectiveness of different court styles?

Mock a murder or other crime and let the law and justice handle it as normal. At the end, reveal the true mock and see how close the law got and how close the court got.

I'm not saying it would be practical and maybe impossible but I would find the results interesting.

That’s really interesting. I do wonder if requiring jurors to write an opinion would have a similar effect, or would it just be like every group assignment in school where most jurors decide to coast off the work of the most diligent member.

That matches the common wisdom I've heard multiple times from those in the know here in the US that, if you have the option of a jury trial or a judge (bench) trial, which is often the case in criminal proceedings, you probably want the bench trial if you're actually innocent and the jury trial if you're actually guilty.

Sure, but what are those systems? Are they like Japan where they don’t charge as many cases, or are they like North Korea where you are executed with a missile (and therefore aren’t innocent in jail). Is it judges or sortition? All of the other cultural context matters.