Many differences, yet purely from a freeriders perspective, to us a few stand out:

1.) The Alps have many more resorts, more lifts and easier lift assisted back-country access.

2.) No monopolies. The lift companies in Europe do not control who teaches or guides on the mountains.

Take Jackson Hole. Amazing place. And very few lifts. Not much around within driving distance. Take Innsbruck: 20 resorts within 90 mins drive, glaciers, glades and endless freedom to choose lines. Go wherever you want, no gates, no questions, no problems. SLC in Utah probably comes closest in the US, several resorts. Having had experience with snow patrol literally chasing me in Alta and Snowbird guarding a small number of weirdly placed back-country gates. Going out freely by ducking the cables is trespassing punishable with jail-time. And the resort controls who guides and teaches. We like the US to ski, snow is often awesome, we love European freedom.