If you can wait for 3-4 months then go for Jazz , it satisfies all the requirements you need!
But if you can't wait you can go for in for i20 also especially with the 50k discount your mentioning! The AC is a bit weak and its not a scorcher , its not a great handler as well. Steering rattles issues , many people have it , many people don't have it. But its a no non-sense car which will not let you down and will take you from point A to point B. Also there is news that a new i20 is coming next year.
I would say you go ahead with Jazz booking , in the mean time when the new i20 arrives , check it out and if you find it satisfactory cancel Jazz booking and go for i20.