I assume you are talking about using such ammunition for practice, rather than hunting, since FMJ bullets are generally illegal for hunting in most, if not all, states.

My experience with such ammunition dates back to my service in the military, but generally we experienced less bore wear and greater accuracy with the steel cored armor piercing ammunition than we did with the lead cored ball. I assume it is because the lead core of the ball ammunition would "set up" slightly while overcoming intertia as pressure built up in the cartridge case, while the steel cored rounds were impervious to the force of acceleration.

The comparable wear produced by the two types of bullets was conclusively proved by the markedly longer barrel life of machine gun barrels fired with AP as opposed to ball ammunition. We always used AP for requalification on the rifle range.

I see no down side to using cheap military surplus ammunition for practice and a real advantage to be gained if it promotes additional practice. Even corrosive ammunition can be used, provided appropriate cleaning measures are adopted and rigorously followed.