I can give you a biased reply - as I have a 4x4 MultiJet and two previous ones too.
There's a lot of 'it depends' comments here. Also, this all assumes you mean a 4x4 Cross (the only model that was available with the diesel). Not all Crosses are 4x4...
Only diesel Pandas after later 2017 meet Euro 6 emissions standards, which means anything older is subject to things like the London ULEZ charge, which other cities are likely to introduce at some point. (Diesels which meet Euro6 and for petrol the older Euro4 standards – which any version of the TwinAir does – are exempt). Vehicle Excise Duty ('tax disc') varies depending on the year, but there's not much in it and equates to about £12 a month for either car.
The diesel will offer much greater fuel economy (easily 55 mpg, and 60 without effort), but that's offset by the added prices (at present) of diesel fuel.
If you won't be making frequent long-ish journeys, the diesel particulate trap will suffer. Ideally a run of 40 miles plus at least once a week is needed. If it's all town driving, TwinAir definitely better. (But if all Town Driving, then why a 4x4...)
The diesel has a lot more torque and at lower revs, so is a better offload option. The TwinAir is (based on views of others, as I've not driven one) tricky around town with its extra-low first gear (to compensate for the lower torque figure). The petrol Cross 4x4 has six gears, but by adding a very low one at the bottom of the gearbox. The top three gears are the same on both engines. At motorway speeds both are doing about the same revs (although 2800 rpm is 'high' for a diesel).
The diesel weighs a bit more (100kg+ extra) but has longer service intervals with fewer parts to be changed. Not a lot in it in on overall service costs though. Anecdotally the TwinAir is very fussy about being serviced correctly (a 'basic' garage may not be aware of some of the extra things needing attention on this unique engine) and with very specific oil requirements. The diesel is a little less fussy here, but eividence of regular oil changes is good news for its timing chain.
Although diesels got a bad press, they still have lower carbon emissions than a petrol. Small turbo petrol engines also have emissions of NOx, but the diesel can generate more particulates (the trap should prevent most of these escaping though). My eco-conscious view is that for my driving requirements, the diesel is a least bad option.
Stand by for counter arguments and a debate...