As a general rule -
Striking arts like muy thai and karate tend to lead to more injuries, especially if you get to the level at which sparring is used.
Grappling arts like judo and jiu jitsu are "gentler" and participants probably get less injuries. That being said, neither are all that gentle, but judo is definitely rougher since it focuses on throws, whereas jiu jitsu is ground grappling mostly.
But, really it all comes down to your approach to it and the attitude of the school you are in. If you go in like a bull determined to learn how to beat everyone in your path you will crush some and you will get beat up in return by others. If you approach it as a learning experience, exercise and fun, and check your ego at the door then you will be much better off. And, I've found in jiu jitsu that schools often have different attitudes. Some are very competition oriented and in training each partner is like a small war to see who is best. Others (the better ones in my opinion) have a more cooperative attitude and everyone tries to help each other learn and progress.
"Nature never hurries, yet everything is accomplished."
- Lao Tsu