Probably not... I believe the Stanton 500-series is about on the sonic level of the Grado Black (and is probably more rugged and durable as well). The Grado Black will be warmer in the midrange, vs. the Stantons which are warm in mid-bass... otherwise they are roughly comparable in quality.
A new turntable is "always" in order for better SQ...

. Or you could just get a new stylus/needle for the Stanton and be happy.