The Mazda 3 is about 6 cubic feet bigger inside than the VW GTI and it's pretty obvious. Still, there is plenty of room in the GTI to haul things with the rear seats down. The Mazda is just a little better in this regard.
Fuel economy in the VW GTI is slightly better than the Mazda 3, but it requires premium fuel. In the end, it's about even.
It's no contest. The GTI is much more powerful and the engine smoother overall.