I think the jazz is better because I found the I20 quite dull to drive. The Jazz is also more spacious and practical and has a better engine too. Also i found the interior better too. but the i20 looks better IMO and is more loaded too.
If you are looking for more of gadgets, bells and whistles, no other to look then i20 which is loaded to the brim, but a no nonsense practical long working horse with honda's gem engine would serve you for years to come, you can never go wrong for honda petrol engines and jazz is a beautiful car with superb engine too.So its your call what your requirement is and take the plundge.
"Honda Cars India has stopped production of the Jazz hatchback in India, in a shocker of sorts. While Honda will service the existing orders for the car, no new orders will be taken. The discontinuation of the Jazz hatchback in India comes at a time when the big price drop on the car effected a couple of years ago hasn’t really done much to boost sales of this outstanding petrol hatchback, which continues to sell well under 1,000 units every month. With no diesel engine in store for the current generation Jazz, selling low volumes the heavily discounted Jazz is said to be infeasible for the Japanese car maker."