What do you value more?

Riding comfort? Fuel economy? Resale value? Cargo capacity?

The Mazda3 HB rides better and has better seats than the Jazz. You'll know this very well if you drive longer distances. Mazda3 also handles better with nice feedback from the car. The Jazz's power steering feels disconnected from the road, kinda feels driving one of those racing video games.

The Jazz (as mentioned above) gets better fuel economy because of its engine and its lighter weight as well.

Honda gets better resale value BUT if you are buying your Mazda3 HB from the used car market, you might actually get a better deal (as compared to the Jazz).

Cargo capacity... its basically a hit and miss here. The Jazz can fit more stuff for a car of its size BUT the Mazda3 HB can still get more things inside simply because the Mazda3 is a bigger vehicle.

My personal choice... Mazda3 HB over the Jazz.