The 370 has a shorter wheelbase than the 350, so is going to feel a bit livelier/twitchier on the road than the M3. That said, the 370 isn't renowned for being the most agile of cars so I wouldn't worry too much about that.
In every way that matters, the M3 is the better car. Better engine, better interior, better drive. And yet, when I moved on from the 350 I bought an E92, hadn't even picked it up and I knew it wasn't the right call, and so got my deposit back and bought something else. Truth be told, it didn't excite me at all, despite being an amazing car. The 370 also leaves me cold, so that may not be saying much. Drive them both and make up your own mind, they're very different and I suspect you'll gravitate towards one or the other very quickly.