There's not a lot in it. You can get such massively better mileage from diesel that it might make up for the extra particulate damage and even the extra N2O emissions (N2O is a much more potent green-house gas). Quoting from Dept. for transport website.
"Cleaner conventional fuels are already on the market: ultra low sulphur petrol (now available in most areas) and ultra low sulphur diesel (now universally available) offer emissions benefits to existing vehicles without the need for any physical modifications.
The relative environmental benefits of petrol and diesel is an ongoing debate. Based on current technologies diesel vehicles tend to be more fuel efficient and emit less carbon dioxide, the main greenhouse gas, than their petrol counterparts but produce greater emissions of particles and nitrogen oxides - the two air pollutants of most concern.
However, emissions from both petrol and diesel powered vehicles can vary considerably depending upon, for example, the standard of engine and fuel used, type of catalytic converter fitted, and type of journey undertaken. Furthermore, as engine and fuel technologies develop both petrol and diesel vehicles are becoming progressively cleaner and more fuel efficient."
So how you drive it, and trying to minimise the car journeys, makes the biggest difference of all.