My experience driving both:
Z4 was very refined, the folding top is cool. The new design is far superior to the old one. The engine is very smooth.
370Z (touring/sport, not the roadster) was raucous, relatively unrefined compared to the BMW.
Both cars handled very well.
I preferred the 370Z. I'm buying one in a few weeks. Why? because the experience raised the hairs on the back of my neck. Fun factor 10 out of 10. That didn't happen with the Z4. It won't be a daily driver, the purchase is just for a toy. If it was a daily driver, I might have gone for the BMW.
Go drive both, it's the only way to make a rational decision.