Each successive version of the Jazz has seen improvements. The only model I'd ever accuse of being harsh was my first but that was the CVT-7 Sport so was designed with a stiffer suspension. The Mk3 does take bumps a little better than the Mk2 but both seemed fine to me.
As regards performance you might want to consider this: The car you consider to be more performant is the car with the worst fuel consumption. For all the advances in automotive technology over the decades one fact is inescapable: If you want more get up and go you have to burn more fuel.
As regards the Jazz though, so what if you have to press the accelerator pedal further? That's why it's designed with that throw, that's why the engine has that range of RPMs. You as a driver are being given a choice - saving fuel or moving quickly. The engine in your Jazz will take everything you can throw at it (especially since it's a CVT). When you want to move shove the pedal down. You don't have to shove it to the floor but be sure you poke it enough to get the RPMs above 2,500. That'll move the engine out of Atkinson mode and you should get all the power you're likely to need on the public highway - in my experience more than most drivers use.
(*)In case you haven't found it yet there is a 'notch' at the bottom of the accelerator travel in Mk3 Jazz. Push the pedal past that point and you'll get the benefit of 100bhp pretty damn fast in the CVT