This mouth guard is made from silicone which works better with braces. Most mouth use plastics which won't fit over your braces as well as this one.

If you have braces, it is even more important for you to wear a mouthguard than it is for other people because of the risk of getting cut. These should provide good protection for you if you wear them right. Make sure to wear both the upper and lower mouth guards, as you said, and if you are still concerned about getting cut, you can show your mouth guards to your orthodontist to make sure they fit you well and are providing ample protection (though these are made to fit easily without boiling and should not give you a problem).

Akiva - yes, mouthguards such as this do a great job in protecting the mouth even when wearing braces. If you have braces on you upper and lower teeth it is generally recommended you choose a double layered mouth guard that protects both rows of teeth rather than just the top layer style.