What’s the difference between the analog & digital outputs on a CDJ1000?

Quite simply one outputs an analog signal and the other a digital signal. Signal from a CD starts as digital signal. It can then be outputted as digital signal or analog. The DJM800 is a digital mixer. It processes all the audio digitally. Any signal entering the unit as analog signal is converted to digital signal immediately. It therefore makes sense to keep the entire signal process digital to avoid loosing quality in the conversion process between each unit.