A Quattro (A8) drives up a steep slippery hill. The all 4 wheels get in spin, the car stops (wheels still spinning) then the engine gets non-responsive, the car is stuck.

Other Quattro –A6 (10 years older) has no problems.

The A6 (’93) feels much more stable, no sliding issues.

Following another A8 proves that the car is not stable on slippery surface- in any turn the rear end slides and corrective measures have to be taken.

It seems like some Quattros are not better than other ordinary cars.

What happens with the collaboration between the quattro, traction control, ESP, EDL, power management?

Is the global stability algorithm effective?

Is the over engineering the cause of A8 failure to perform up to the expectations?

The A8 weighs a great deal more than a 93 A6, none the less i have never run into a hill i couldn't climb in any audi i have driven. What kind of tires are on the A8? You have at least all seasons right?

Tires are Toyo Versado LX- 5k old.

My guess is that due to engine power a learning to drive in real winter is necessary.

Nonscense, it you aren't going anywhere then it could be a problem with the stability control. Did you try turning off the ESP?
The toyo versado lx is a touring tire! They aren't even supposed to be on the snow.
You need a set of Toyo snowprox S952 tires, those will plow through everything. You should also check the fault codes in the brake electronics.