Not sure how you narrowed your options down to these 3, but Le Melezin in Courchevel is a clear winner in that race: world class skiing and the Aman brand/amenities. The Chedi would be my second choice, but Andermatt is quite remote, and the town itself is neither charming nor upscale (yet - the Chedi is the first component of a planned megadevelopment). Gstaad is not a location for serious skiers IMO, so the Alpina comes in last. There are some decent runs nearby in Schönried for example, but you need to drive there.

Finally, since 2 of your 3 choices are chain hotels, I do feel duty-bound to stress the fact that most of the top hotels in the Alps are independent properties, or part of small chains such as Sibuet.