This thread
http://clubjazz.org/forum/index.php?topic=8719.0 contains some relevant discussion. I changed from the Mk 3 Jazz to the HR-V about 6 months ago (and before that had a hybrid Jazz). I'll make my comparisons with the Mk 3 since that's what the HR-V is based on and I'm also comparing the CVT SE versions of each.
Pros:
1. The HR-V's engine isn't much bigger than that in the Jazz but behaves as if it is a lot bigger. The engine on the Mk 3 is set up for the more economical Atkinson cycle in the lower half of the revs range (and has to rev above around 3,000 rpm to deliver useful acceleration) but the HR-V's engine is much more progressive in its performance and capable a smooth gradual and quiet acceleration at around 2,000 rpm.
2. The windscreen glare problem which really annoyed me on the Mk 2 Jazz and was still (but reduced) problem on the Mk 3 is not an issue on the HR-V with its steeper windscreen.
3. More capacious cargo capacity in the HR-V. I recall that someone traded in the Mk 3 Jazz for an HR-V because the Jazz wouldn't take a set of golf clubs in the boot. The HR-V will take up to 5ft long objects with the rear seat folded and it's possible to get 8ft planks in if the front passenger seat isn't in use.
4. Useful details such as the ability to fold the mirrors using the remove control plus the nearside mirror automatically tilts downwards to shw the rear wheel when reversing.
Cons:
1. The HR-V is thirstier. I'm assuming about 20% thirstier until I've clocked up a year of motoring under similar conditions (but have to admit that I tend to drive the HR-V a bit faster than the Jazz which won't help the mpg). However, the HR-V's fuel tank is 25% larger so there's no reduction in range between refills.
2. The touch panel for controlling the heating and ventilation is a challenge to operate safely as it's necessary to look at it to change anything.
3. While the HR-V rides better, I'd much prefer a size smaller wheels with correspondingly larger tyres to help damp out the potholes. The big wheels + lowish profile tyres look nice but aren't the best for the deteriorating UK road surfaces.
4. Niggling software issues such as the temperamental auto idle stop and the whole touchscreen system (but the Mk 3 Jazz also has these problems).
5. While there's some useful space and a decent selction of sockets under the centre console, it's an awkward location for access when sitting in the front seat.
