Well of the resorts you've mentioned, I've been to Engleberg and Andermatt but not St. Anton. I've never been to Laax or Aspen. But I've been to Vail, Beaver Creek, Araphoe Basin and Wolf Creek in CO and I've been to Alta in Utah.
In the weeks I've spent in CO, I have always had dumps of at least a foot or more of light fluffy snow. In Europe I have occasionally had huge dumps of heavy snow, and even more rarely a dump of the soft stuff. I skied maybe 7 weeks in the alps this season and I didn't get one day of really perfect soft pow. Don't get me wrong I had an amazing season with great dumps but the dumps were mostly heavy snow more akin to California. On the day I arrived in Saas Fee in March, there was a meter of fresh snow, and an empty resort because the roads were closed. It was an incredible day but the snow was fairly wet and heavy.
The terrain is different too and I didn't mean to suggest the gnarly mountain lines don't come with great snow sometimes but in CO you do get 1000m vert (roughly) of powder slopes and glades that go on for miles wide. And when that is covered with a foot of soft stuff every week or so then that works for me.
I am not trying to knock Europe, the alps are incredible and I am lucky to ski there so much. In Colorado I just feel like I more consistently get the snow I want to ski the most, and Utah is just better again.
Of course you can have the trip of a lifetime in Europe, but to guarantee a day of that fluffy stuff, you need to be there for a long time.
I guess what I really mean is that.. in Europe you can get some of the very best skiing the world has to offer, but you are less likely to get the conditions you dream of. In CO the skiing is less exciting, but your chances of a really good day are better.