While I was in the U.S. I spent a few days in Colorado and had the opportunity to ski one day at Keystone (I'd been there once or twice when I lived in Denver, but it's not one of my old haunts). It was great fun to go skiing in Colorado again, after having become accustomed to skiing in the Alps rather than in the Rockies these last few years. It was also a reminder of the many differences between skiing in North America and Europe (although maybe I shouldn't lump everything together, and more specifically say Germany/Austria). One would think that skiing would be a fairly homogenous activity the world over, right? Not so.
There are several major differences:
1. "Off-piste" Skiing
The biggest thing that I had to get used to regarding skiing in Europe is that skiing "off-piste" is a really big deal in Europe. The majority of skiers only ski "on-piste" - meaning on marked, groomed runs, and they never venture into the trees, the back bowls, or the bumps. Interesting that Americans don't really have any phrase so clearly distinguishing the two, isn't it? In North America it's all just part and parcel of skiing, and once you reach intermediate level, of course you are also venturing off the groomed areas. This on-piste/off-piste dichotomy was baffling for me at first, because a lot of these guys are good skiers and they could ski off-piste, they just don't. I still have a hard time understanding this sometimes because skiing powder is an experience unlike any other... much as I love a good, groomed, speed run, there's nothing like floating through a blanket of fresh powder.
Part of this is cultural. The average skier in Europe is more risk averse and they are taught to fear the deep snow and bumps.
But I think more of it has to do with the design of ski resorts in Europe versus in North America. In Europe, anything off the trail is out of bounds, completely uncontrolled, and lacking in signage. So if you have an accident on-the-trail vs off-the-side-of-the-trail, it is my understanding that the "rescue" costs can vary greatly. In North America, ski area boundaries include everything inside the outer boundary, and ski areas pride themselves on their moguls, their huge bowls, and everything in between. It's what distinguishes one ski area from another. These areas are also well-controlled, avalanches are shot down, and potentially dangerous obstacles (e.g. cliffs, streams, large rocks) are often marked or there is at least a sign at the top of the hill warning skiers to watch out for such obstacles.
I think there are some practical reasons behind the design of resorts. A lot of the European resorts seem to be built adjacent to private property (people can own homes literally on the side of the ski runs), whereas the resorts in North America are often carved out of national forests or state-owned land. Also, I wouldn't be surprised if the respective legal and insurance systems impact the "perceived risks" related to skiing, thus affecting cultural norms.
In general though, there is an advantage to being a brave, off-piste skier in Europe: not as much competition for fresh pow! Sometimes, even the snow patches in between runs are almost untouched and pristine - for days after it snows. The drawback: it's hard to find ski buddies who will venture off-piste with you.
2. Lift Lines
Lift lines (if you would go so far as to even refer to them as "lines") in Europe are chaotic and uncontrolled. Ski tickets are all electronic and everyone shoves forward in a mass, throwing themselves in front of their competitors to get in the gondola first (hint: always go as far to the right of the line as possible so that you can get in the gondola as soon as the doors slide open).
Austria is both more advanced, and less advanced, at the same time. The hills are still covered with t-bars (long, slow, cold hell), but there are few of the old, slow 2-person or even 4-person lifts. It seems Austria skipped straight into modernization, going directly from t-bar to high-speed 6 and 8-person lifts, and gondolas.
4. Après Ski
Skiing in Europe is as much about the party as the actual skiing. Ski areas are known for their après ski scenes, and many people choose their destination as much for the reputation of the party at the end of the day as for the terrain and challenges of the slopes. Some of the ski towns in Austria are huge party towns, despite their otherwise charming, idyllic appearance.
In this way, skiing is more inclusive in Europe, because you don't have to be a super athlete or thrill seeker to take up the sport. It is perfectly acceptable to spend more time at the après ski, or even just sipping a hot chocolate with rum inside a warm lodge.
Lots of people don't even bother skiing. They just buy a roundtrip ticket on the gondola and spend the whole day hanging out on the mountain - without the skis.
5. Ski Lodges
In the U.S., ski areas try to channel the rustic "country" charm that is associated specifically with the American West. Lodges are usually large, open log/wood/stone structures with soaring fireplaces and main halls filled with tables. Skiers often bring their own lunches, or they buy from the cafeteria. There are always drinking fountains in the lodges where one can fill up a water bottle. Lodges are usually at the top and bottom of the mountain, and most ski areas have one or two smaller lodges tucked away in a back area, where the locals and more adventurous skiers inevitably head for their midday break.
In Europe, the "lodges" obviously have more of a European flair, and I would suggest that there are usually more, smaller, lodges scattered around a resort. It's not unusual to find a little Glühwein hut tucked away off the side of a run somewhere. Also, some of these lodges can be quite fancy with restaurants, bars, and even overnight accommodations.
Europeans are sun worshippers, and you will find people outside on terraces, heads tipped back, soaking in the sun, even on the coldest days.
6. Ski Food
Some of these "fancier" European lodges also lend themselves to a higher quality of food- they are well-known restaurants with highly esteemed chefs. As such, it can also happen that it's not allowed to bring your own food (though the outdoor tables are always open to picnics).
There is also a "ski cuisine" that can be found throughout Austria - regardless of where you go, you can always find sausages and fries, a couple types of soup (usually gulasch, potato soup, and/or lentil soup). There's usually spaghetti, Schnitzel, Currywurst, and for a sweet meal, Germknödel or Strudel. Of course, there is always beer, Glühwein, hot chocolate (with or without a shot of rum) and espresso.
U.S. ski food tends to be burgers, fries, pizza, soda, etc; the typical American "fast food / junk food" fare. Brownies, cookies, and hot chocolate are also high on the ski food hit list. Many resorts are getting more and more options though, adding in things like burritos and tacos, and Asian-inspired dishes. There is no typical "ski cuisine" that I can discern in America... that's kind of sad actually! We do like a beer post-skiing (especially a good micro-brew), but drinking with lunch in the middle of the ski day is not so typical.
Whereas snowboarding is probably more popular than skiing in America, in Europe you find far fewer boarders. There are still excellent terrain parks, but skiing is by far more popular than snowboarding, even amongst young people (maybe this is connected the fact that most people remain on-piste, which I would argue is generally better for skiing than boarding?).
In the U.S., I love skiing up to a lift where the lift operators are blasting out some of their favorite tunes. It's usually some laid-back reggae, classic rock, or folk rock. Good stuff. You don't hear as much music on the slopes in Europe, though some of the lifts will have a speaker system, and of course as you approach the end of the day and the après ski gets going, the party music echoes off the hills... but it is that type of kitschy-club music (they love to take 80s songs and put it to a techno dance beat, and then intersperse those songs with favorite German/Austrian dance hall songs).
Skiing is twice as expensive in North America. Most day rates run over 100 Dollars, whereas prices in Austria are just over 40 Euros for a day pass. Rental prices and food are also higher. It's an expensive hobby (or lifestyle, depending upon how you view it)!
But... there are also way more deals in the U.S.
If you know a local (or you are a local), you can usually find some amazing deals (e.g. discounted season passes sponsored by local businesses, "partner" discounts if you go with a season pass holder, mid-week specials, "kids ski free" deals, etc.). Europe is not known for its amazing discounts. It's also usually not worth buying a season pass to a resort in Europe, because the savings are minimal.
10. Ski Resort Size
Europe is full of lots of small ski areas, many of which have been linked-up to form a larger resort. North America is the land of mega resorts -- it's hard to find a parallel over here. It seems more essential in Europe to try lots of different areas because of this- there is more propensity to run out of new terrain quicker, and get bored. At place like Vail or Whistler, one could easily ski for an entire week and feel like she had barely begun to experience all the resort has to offer. But for a newbie, that vast size can also be intimidating! So it all depends on what you are looking for...