Short version: there's no one style, or school which you will find adequate data to make a useful comparison, there are, however, instructors and methods which are safer vs. more dangerous.
Safety as a Goal
The first thing to understand is that what we're talking about is harm reduction. The goal is to reduce injury and harm within reasonable efforts. Part of this is figuring out acceptable risk and acceptable effort.
A basic tenet is understanding that there is a huge difference between minor and serious injuries, and that if your training causes minor injuries but improves your odds of avoiding serious injuries (or death) then it is typically considered a worthwhile tradeoff.
Minor vs. Serious Injuries
Minor injuries are those which typically resolve in a few weeks, and lingering effects are gone in a few months, at the worst, without the need for physical therapy. This includes bruises, most muscle strains, minor sprains, cuts, and the lightest end of concussions.
These are common in any physical activity, and also can be incurred doing normal daily activities, such as lifting something incorrectly, slipping on stairs, or bumping your head while getting something out of the car.
Serious injuries may require months or years of rehabilitation, surgery and may never be "right" again. Joint injuries to the hips and knees, disc or ligament injuries to the spine, heavy concussions, shoulder girdle separations, are the common ones in martial arts training.
These injuries cause lasting problems for the rest of your life, and so, are what you really can't afford to incur during training.
Sorting Data for Martial Arts & Self Defense
Problem #1 - the best studies you'll get will be based on sports training, not self defense training. Sports tend to incur greater rates of injury overall, since they're always pushing the envelope of capacity (in comparison to other forms of training for high-risk work, such as fire fighters or police officers, which requires intensity above a given average but not necessarily the edge of what a person can do.)
Problem #2 - does the given study break out what kind of injuries you are looking at? Most people, faced with a sprain, will seek medical attention (and, if it's happening in a competition, they may be forced to per the rules and insurance requirements of the event itself). Does that get noted as to the type or does it just get piled into "X% of participants needed to go to the hospital"?
So, as you can see, finding good data is very difficult here. Not only that, the biggest difference is in the quality of the instructor you're working with, more than a "style" generally, as to the safety.
For that reason, I usually tell people to talk to students under a given instructor who have trained for 6 months or more, and focus on finding out if anyone has suffered concussions, knee injuries, or back injuries, especially focusing on students who are training to the level you expect to train at ("I do 2 classes a week", "I'm here everyday", etc.). Sometimes a given training regimen is safer for people doing the extra conditioning, sometimes less so if people are over training.
It's also useful to find out if your instructor has any sports medicine and first aid background. The ability to assess how fast to bring someone into certain types of training vs. hold them back to better develop safe skills and/or conditioning to protect against injuries is critical. (See: "Heel Hook Injuries" in many grappling schools as an example of doing it wrong).
Sorting Data for Risk
While it's easy to find national data in most places, what you really want is city or neighborhood level data. In some places you can find crime maps that literally point out what streets or even times crimes happen around you. In some cases, these are easy to avoid ("Pool Hall, 2 am").
The second thing to look at is demographics of who is targeted. Most of the "Rah-Rah Self Defense!" crowd is made up of people who are the lowest risk demographic for actual danger. Again, you'll want to find some way of figuring out what crimes involved serious or minor injuries, if possible - robbery with no injury or "being pushed down" or such aren't really a big problem compared to knife attacks or group beatings.
If you know what kind of risks are most likely, you can tailor your training around it. For example, many countries have few gun attacks because guns are rarely available - in which case knives, sticks and group attacks should make up the bulk of your focus. In places like the US, guns are quite common, and consideration has to be put into that.
Training more risky than attack?
Obviously, any training has risk. The question is whether you're racking up minor injuries which are annoyances but not a serious life impact, or if you're risking permanent injuries which impair your ability to go about life and protect yourself. The former is totally acceptable, while the latter is not.
For some people, self defense is a theoretical exercise - they aren't really at risk, so it's effectively a fun hobby for them. For others, it is a practical question which they are quite at risk, and sometimes even if they aren't attacked directly, having extra capability reduces their stress and worries as they try to live life.
So what can we do to reduce risk in training?
- Instructors educated in sports medicine and first aid (or have access to someone who is)
- Utilize high intensity training at appropriate intervals, with safety gear
- Close assessment of student capabilities - not pushing people too fast or too hard in ways that open themselves up to receiving or creating serious injury
Unfortunately, as I've pointed out, the data is quite shakey and incomplete, there is no standardization in training or assessment of instruction quality. You'll need to do local research and interviews and see whether you can find people with serious injuries or not.