Newer diesel engines have MUCH higher fuel injection pressures. Old diesel injected fuel at around 2,500 PSI or so. TDIs and CDIs use pressures of 17,000-30,000+ PSI. Higher pressures allow for better atomization of the fuel in the combustion chamber, which gives a more complete and better controlled burn. This gives more power, better efficiency, and cleaner emissions.
Some of the old diesels were turbocharged, others were not. There are still non-turbo diesels today, but all TDIs are turbocharged. The newer style turbochargers (VNT, Variable Nozzle, Variable Geometry, etc...) are much more efficient at giving a lot of boost at low speeds, while not overboosting at high speeds.
Electronics have a lot to do with the increased efficiency and power, and the lowered noise and emissions of modern diesels. There are many sensors on TDI and CDI engines, and they all feed into the main computer (ECU). Most, if not all, modern diesel engines are drive-by-wire, where the "gas" pedal is not connected to the engine at all. It is electronic, and tells the ECU what you want to do... then the ECU decides how to do it.
