The i20 is more feature packed whereas the Punto excels in the driving department. Like almost all Hyundai cars,the i20 too suffers from dead steering response(Which feels vague) and a sad suspension setup from handling point of view.I thought they would have improved it but unfortunately they havent.
As for the Punto, since it is essentially an european car, it has a better suspension setup and the steering feels connected to something which is confidence inspiring.Let's face it, the Punto will eat the i20 for breakfast when it comes to handling.
Overall Hyundai has better ASS backup compared to Fiat so in the end, I would say go for the i20 for features and peace of mind in terms of ASS but if you are an enthusiast driver, you will be a bit disappointed with the handling of the car.
Choice is yours in the end!