I had a 370Z. Basically the same chassis with a bigger engine.
Feels like sitting in a bathtub. It's got a heavy ass flywheel that makes the V6 feel as smooth as a V8, but with predictable effects on responsiveness. You can cut the fly weight in half and it's still perfectly good to run on the street without issues.
I traded it in for an Miata NC and never looked back. Sure, the Z has more power, but it doesn't make good use of it the way a Miata does.