From my experience, Jazz wins! main reason being less problematic. My dear Dad was a big VW fan and with the dealership 5 mins away, he brought a Derby in 1980 and then a used one for me in 1985, later a Jetta and a Polo Coupe. Unfortunately, the cars used to break down but worst of all, vw dealers couldn't fixed anything and worst still, used to create more problems, e.g., scratching the bodywork etc. In 1994, when I was able to afford my own car, I brought a new Civic Bel-Air and sold it in 2012 with 105,000 miles on the clock. I couldn't believe how reliable it was and dealership was excellent.
Fast forward, I now have a 2009 Esi i-shift and a manual Seat Ibiza SE, both with same age and mileage. Engineering wise, the Jazz is much more refined-engine runs smoothly compared to the Ibiza. Cost cutting wise, although plastic dashboard is not nice, at least they have a bit of cloth in the door cards, unlike the Seat, plus you get more equipment with the Honda. Further, the engine bay in the Ibiza is so cheaply finished, I always cut myself just by changing a light bulb! I am a driving instructor and realised the Spanish car costs more to run due to more problems, e.g., fan motor, alternator, O2 sensors, door lock and windscreen washer motor all needed changing. The only thing that went on the Jazz was the i-shift actuator, £350, over the same period. Dealership wise, I am with an independent garage now but I would say Honda dealer aren't as good as used to be, but according to surveys, they are still way ahead of VWs/Seat. Design wise the Ibiza looks nice both in and out but the Jazz offers more practicality.
Although the newer VW Golf is nicely made, what put me off was the lack of standard equipment-leather steering wasn't standard!! Personally I will have a crack at the Jazz. If you don't like it, then change it back to VWs as the former holds its value Just make sure you don't go for the DSG gearbox if you go back to a VW!