DI engines provide significantly better efficiency than an IDI engine. The efficiency loss in the IDI engine is due to heat loss from the added surface area of the prechamber and from pumping loss in moving the air into the prechamber and combustion gasses out. The loss is generally figured at about 15%. The heat loss in the IDI prechamber is also the reason that they tend to be more difficult to start, making glow plugs necessary for for cold starting even at relatively moderate temperatures. The VW TDI does not require (or use) the glow plugs until about 9ºC.
Beyond the obvious advantages in efficiency and starting performance the DI engine has some drawbacks. Mixture formation in the DI engine must occur in the main combustion chamber, turbulence must be induced by the shape of the piston crown and the intake port and is somewhat lazy when compared to the violent turbulence generated in the IDI prechamber. Charge mixing during injection depends largely on high injection pressure and is aided by turbulence. In the IDI engine the opposite is true, good charge mixing in the prechamber is due mostly to turbulence, injection pressure plays a minor role. IDI engines often have better air utilization rates than DI engines and due to their superior charge mixing can continue to produce torque at higher speeds than DI engines. The IDI engine also tends to be slightly quieter and a bit gentler on lower end components than the DI engine due to softer pressure rise in the main combustion chamber, though the VW TDI has overcome the noise issue with better sound insulation and 2 stage injection.
In the end, the DI engine wins in the passenger car, where efficiency is of paramount importance. If your goal is ultimate performance, the IDI is certainly worth a look. It may actually have more potential if developed to the same degree as the DI engine.