Sadly the Audi engines are not as efficient as the BMW engines. quattro also results in a substantial reduction in MPG.
The later engines are not as economical as the earlier engines. The reason is the stricter emission standards. We;ve gone from Euro3 to Euro4 to Euro5 standard engines in the last few years. We all know about DPF's - these are 100% required to meet Euro5 standards. They also increase back pressure in the exhaust which reduced the pressure across the turbine which costs power and economy.
The other requirement is the reduction in NOX production. To achieve the highest thermal efficiency, i.e. power and economy, the diesel needs to be injected at a specific point in the engine cycle. This point generates the highest cylinder pressure and the hottest most efficient burn. Unfortunately, this point also produces more pollutants in terms of Nitrogen oxides. Later cars are calibrated with retarded ignition timing - specifically in the mid range, in order to meet emission requirements. With a careful remap you have the option of optimising this timing and bringing back your lost economy.