I have difficulty in believing that Honda's 3 cylinder turbo which is due to show up in the Civic shortly won't also appear in the Jazz in due course, which would explain why there's currently only one engine option. A 3 cylinder turbo would have the capability of both better performance and better economy (but maybe not both at the same time) compared to the current engine so it will be interesting to see how Honda will play their options. Eco setting by default with a "sport" button would give the most favourable results in the standard tests.
There is the residual uncertainty about the longevity of the small turbo engines so the 4 cylinder non-turbo might stay on the line-up for a few years so that purchasers have a choice. I personally find this engine to be smooth and refined. There is the well-discussed tendency to rev (when coupled with the CVT gearbox) on initial acceleration but maybe that is to remind people that there is an engine because, for the rest of the time, one doesn't hear it.
The Mk 3 doesn't currently score well on value for money and one has to wonder if Honda isn't trying to shift large numbers of these vehicles in the UK. I wonder how busy the factory is? However, provided residual values stay good then paying a bit more is less of an issue.