Over powering the ski (for me anyway) happens when the ski is too soft for the conditions/speed I'm skiing, and the gives a perceptable feeling of wanting to fold in half. The front of ski will hook violently under me, causing the skier to get thrown or, if you can react quick enough, causing you to skid the tails to maintain control. I found that a ski like the Volkl 5* would fold abnormally about 1/3 of the way back at speed. I think a lot of people found this issue with those skis, and that's why they came out with the 6* the following season, which had a much stiffer forebody. The issue then became it's ability to handle bumps with any forgiveness. If you weren't on your game, the ski would over power the skier and turn into a springboard as it went up the front of a bump, sending you on your backside.
Overpowering the snow is when you are trying to carve (or close to carving), and the snow does not provide enough lateral resistance to keep you in the path/arc you were traveling, and the entire ski, from tip to tail, starts to push the snow out sideways. This happens all the time in soft snow, and is the reason that it's not possible to carve a pure arc in soft snow. If you were racing, and had your hip 2" off the snow as you were rounding a gate, and the snow surface got soft enough to over power it, your feet would come out from under you. As an analogy, think of a mountain bike doing a 2 wheel power slide around a turn, vs carving a clean track around a turn.
If the ski only washes out in the tail, but the tip stays in the intended line, that's usually operator error or the ski being overpowered, not the snow.