Either will work.
The lugs are there to fasten the stock to the barrel not the barrel to the stock so the brass is more than strong enough to do that.
Curious though, why not use the staples. They are HC, work fine, are somewhat easier to install (although the first time the "fear factor" of accidentally drilling into the bore is way up there - although no worse than buggering up a dovetail - going too wide or too deep).
The only place I use "lugs" is on swamped barrels because you can't drill into the waist - in fact you can't dovetail either so they have to be soldered on. And I won't mix lugs and staples.
If using lugs I generally go with steel - just because - never really sat down and thought about "why". I don't see an "advantage" to using one over another.
On a probably "doesn't matter" note - dis-similar metals can react to each other under some circumstances. Boat builders know this and wouldn't mix brass and steel due to the possibility of "galvanic corrosion" where one metal starts "eating" the other (not really, but best way to explain the result).
Don't know if this would apply to a rifle barrel, but given there are some "brass" barrels out there, I might tend to use a lug of the same material as the barrel :idunno: