The AVR's are traditional designs employing ADC's, DAC's, and analog amps. The new DPR's use a digital amp module from D2Audio. There may be ADC's in the signal path depending on the input, but the DAC is the power amp itself.
Ideally, you want to input a digital signal, which will pass through the DSP and then will be converted to PWM for amplification. The theory is that as the signal is in a digital state, it is less prone to corruption that can happen in the analog domain.
Here is some additional info on the DPR's. I'm interested in them as well. I have a cheap little Panasonic with digital amps(although they use a different digital amp chipset)that sounds remarkably good, so I'm sold on the digital amp idea, however, I like the fact that the HK's are at a higher price point, appearing to make less compromises in the design.