Nylon, good for scrubbing the bore that is not leaded, little chance of bore damage. Good for working with copper solvents.
Brass, good for fouled barrels (not copper fouling) and they have been around for ever. Some chance for bore damage if applied with a lot of vigor.
Stainless steel, works well on both lead and copper fouling but can/will damage bores in a short order. I have been advised by several bench rest shooters not to use them.
When buying brushes try to get those that are for only one caliber. If you have a .45 get .45 brushs not .44/.45 brushes. They will work well with the smaller caliber but not so well with the bigger size.