I have an LK style Classik Music K and the newer version. Sound quality wise, the newer one has a brighter, more detailed sound than the older model.
As has already been mentioned, the newer Classik has digital as well as analogue inputs, but the older one has a clock/timer.
The old Classik is much better to use. It responds more quickly when you press buttons. The new model uses a CD ROM drive as you would find inside a PC, whereas the old one has a proper mechanism. This means that the new one will be easier to service, but also means it can take around 30 seconds between loading a disc and playing music.