The Mazda2 is more fun to drive and more refined... and quicker in 1.5 AT than the 1.3 MT Jazz... it may be an MT, but the gearing is still long for the engine.

The Jazz wins in terms of space and practicality, though... and it'll be a bit more economical thanks to the MT. (I say a bit because I was disappointed with the 1.3 AT economy versus 1.5 ATs)