Different types of cars. One is a FWD hatchback that handles well and performs competently while being practical. The other is a RWD two seater with little truck space.
If you live somewhere where it snows in winter or rains a lot, get the GTI.
The GTI also has back seats and a large trunk and better fuel economy and low maintenance costs.
The 350z only seats 2 people, is RWD, and has a very tiny trunk.
I have driven both cars and they are equally fun. The 350z is much faster, but the GTI is the smarter choice. I would go with that.