The cars which I compared to Honda Jazz in this category are Hyundai i20 elite and Maruti Baleno. I have briefly compared the petrol versions only.
The advantage with i20 is the various types of gadgetry which they provide in the car. However, the advantage with Baleno is the price point.
According to me Honda Jazz scores over both the above cars in space, design and the engine, which is super quiet. Sales and after sales service of Honda is also excellent. If you have money to spare I will recommend you to go for the cvt version. Fuel efficiency in manual and cvt version is also good