I asked Alessandro about this. He replied that his Music Series sounds a little more neutral and open than the Grado counterparts. How big is the difference? He said some people hear a big difference and some hear little or no difference. He said the Music Series is designed for music-industry professionals like sound engineers and so must avoid the colorations of the Grado, which is designed for the hi-fi crowd.
I imagine the magnitude of the difference one notices depends on source and amplifier, how well trained are one's ears, and how badly one wants to hear a difference. From what I've read on this forum, everyone who's owned the MS-Pro has really loved it.
In the Grado interview, Grado says the Alessandro cans use different drivers, so there are real differences, not just different branding.