Diesel fuel has historically been cheaper in Europe due to lower taxes, and as a result there has been a big increase in the market share of diesel passenger cars. That said, some governments are trying to reverse this; notably the UK, where fuel taxes are significantly higher on diesel fuels and vehicle annual registration fees are higher for diesel vehicles.
To an extent, this is due to concerns over particulate emissions. DPFs are now mandatory for all new model diesel cars in Europe. They are expensive and bring a lot of problems (poor fuel consumption, high exhaust gas temperatures, occasional clogging unless regularly given high-speed highway driving, and very high sensitivity to engine oil - use of engine oils with traditional anti-wear and anti-corrosion additives will irreversibly clog the filters due to ash particles produced by the combustion of these additives).
There is also potentially the ongoing cost of regular refilling of the car's DPF catalyst solution. Not all cars use this, but some DPF systems are designed to work with a fuel-borne catalyst (usually cerium oxide nanoparticles), and the cars come from the factory with a concealed reservoir of catalyst which is dispensed into the fuel tank when you fill up. After about 40k miles the reservoir depletes, necessitating a very expensive ($500+) refill.
Similarly, because of the complex emissions systems such as EGR systems, diesel vehicles are generally less reliable than they used to be. Similarly, modern common-rail fuel systems are much more sensitive to fuel quality than they have ever been.
I'm not aware of any passenger cars using urea solution (DEF) for NOx control, EGR is the preferred method in Europe; the use of urea was considered too inconvenient for use by the general public. However, urea is used for heavy trucks, buses, etc; at a truck stop gas station the pumps often have 2 nozzles, one for diesel and one for urea; just fill up both tanks at the same time. That said, even if you run out of DEF, the vehicle will still run, but power will be limited. Urea is purely an emissions thing; it does not effect engine running and lack of urea will not damage the catalyst. (Emergency vehicles like fire and ambulance are often fitted with an override system which will prevent the ECU entering reduced power mode in the event of urea exhaustion; of course, if you grease the right palms, you can get such an override installed on your truck too).