Battery acid is sulphuric acid, H2SO4.
HCl is basically turning the copper in the brass to a salt, copper chloride (CuCL), while the hydrogen peroxide acts almost like a catalyst.

So we have Cu (copper) reacting with HCl (hydrochloric acid) and hydrogen peroxyde (H2O2). This gives us molecular hydrogen (H + H -> H2), water (H2O) and copper chloride (CuCl).

It's been a while since college chemistry, but that should be it.

The chloride in the ferric chloride solution (a dissolved salt) is dissociated in Fe+ and Cl-, again, another donor of chloride, but not so reagent as HCl and with that nasty iron wanting to stick to everything, like clothes.