Brass brushes are ideal for use with solvents designed to remove powder, lead, metal fouling, carbon deposits, and rust. Nylon is also a great choice when cleaning with solvents like copper removers, as the chemicals won't break down the nylon the same way they might brass
Brass brushes are softer and so won't scratch some grill types, such as cast iron ones. They're a softer brush, which does mean they'll wear out quicker. Steel brushes on the other hand can be used to lower cleaning times and clean hardier grills, such as stainless steel grills.