I've just bought a GT86, it's a great little car. Seating position is so much better than the 350 (not driven a 370, but don't imagine it's much lower).
It's brilliant round corners, stupidly low COG and decently low weight makes sure of that. It's true you can't just get the arse out round every bend, but why would you want to on a public road anyway? Odd bit of sideways action when conditions allow is fine. I also find the gearbox a load nicer than the zed one.
Noise isn't great, it does just seem to get louder as you get through the revs. But that can probably be sorted at the same time as sorting the torque dip at 4k.
It's slower than most current hot hatches, but then so is a stock 350. I'm not a traffic light GPer anyway, so don't remotely care.
You could probably just swap the final drive to a shorter one to give you more torque to the ground, but then you wouldn't be able to get 40+mpg down the motorway.