I know Diesel technology has been discussed a bunch of times in this forum, but just a couple of points to reiterate and some general thoughts;
Motor sport is a showcase for contructors to demonstrate their areas of expertise. So Audi (and Peugeot) would not be developing diesel engined vehicles if they didn't think they would sell more cars as a result... and therefore I think they must think they can win with these engines.
M3 lover; diesel fuel has a higher density than gasoline; therefore a full tank of diesel fuel will weigh more than a full tank of gasoline; However, engines work on mass of fuel (not volume), therefore this is a way to put more energy into the car.
Because the fuel is less volatile than gasoline it requires the extremely high injection pressures to atomise it so that combustion can occur more quickly and more completely in the time permitted.
The thermal efficiency (ability to use the heat energy produced by burning the fuel) of diesel engines it greater than for gasoline engines, so they are, in general, more efficient engines.
In general the torque produced is greater than for a gasoline engine; although it is an oversimplification, torque can be considered to be force x distance. Because the compression ratio in a diesel engine is typically 15 - 19:1, versus 10:1 for a gasoline engine, the the distance travelled by the piston per stroke is greater and thus the torque of the engine is higher. And therefore the ability of the engine to do work is greater, per rev, in a diesel engine.
But... they are unable to rev as high, and because power = torque x revs, even though the torque is higher the rev limit (imposed by piston speed and ability to burn the fuel) means that such engines tend to have lower maximum power than their gasoline equivalent.
The engines have to be built more strongly because the cylinder pressure is higher and the torque is higher. Therefore the diesel engine will always be more heavy than it's gasoline quivalent
Just to answer Toms point about chip fat; No doubt that the engine could run on it; the question is whether the fuel pump would work (for long!); the lubricity (ability to keep metal surfaces apart) would not be there. Furthermore, very likely the injectors would start to foul and the combustion efficiency would drop off. Finally, all the left over bits of fish batter and bits of chip would block the filter!! - furthermore, the smell would have all the fans making a bee-line for the fast food outlets, so all the spectators would leave the trackside...
As a side note; the Shell GTL (Gas to Liquid) technology is a clever bit of chemistry to make synthetic fuels with highly specific and constant properties from natural gas. They are building a couple of GTL plants in the middle and far east and have been running a couple of London Buses on the stuff for promotion purposes.