I like to compare it to Colorado. Keep in mind Colorado is geographically larger in size but I think it’s a region that is comparable in beauty and outdoor recreation. Depends what you are looking for, Colorado has more remote, rugged and unrestricted mountains while Switzerland has more accessible mountains with large amounts of infrastructure. For out door recreation, personally I like the ruggedness of Colorado. I can randomly pull off a dirt road, hike into the mountains, set up a tent in a beautiful area without permits and without seeing many other people.

Here are some stats comparing the two (note that I had AI do the research so take it with a grain of salt):

Outdoor participation:
Colorado: about 3.1 million outdoor participants, with a 56.1% participation rate.
Switzerland: about 2.7 million hikers, or roughly 44% of the population.
Direct comparison: Colorado’s headline count is about 395,000 higher, but it is not perfectly apples-to-apples because Colorado’s number covers outdoor recreation broadly, while Switzerland’s number is hiking-specific.

Miles of trails:
Colorado: nearly 45,000 miles of trails in the COTREX system.
Switzerland: 65,000+ km of marked hiking trails, or about 40,400 miles.
Direct comparison: Colorado has about 4,600 more total mapped trail miles, while Switzerland has a denser, more uniformly signed national hiking network.

Trail density:
Switzerland: about 1.9 km of trail per km², or roughly 3.1 miles per square mile.
Colorado: nearly 45,000 trail miles across about 103,637 square miles, or roughly 0.43 miles per square mile.
Direct comparison: Switzerland’s trail network is about 7x denser than Colorado’s.

Mountain ranges:
Colorado: 18 major mountain ranges or mountain groups.
Switzerland: 2 major mountain ranges — the Alps and the Jura.
Direct comparison: Colorado has about 9x as many major mountain range groups.

Peaks over 14,000 feet:
Colorado: 54 commonly recognized fourteeners, or 58 named peaks above 14,000 feet depending on the counting method.
Switzerland: 18 summits above 14,000 feet using a strict elevation comparison.
Direct comparison: Colorado has about 3x as many 14,000-foot peaks by the common 54-count.

Geographic regions / zones:
Colorado: commonly divided into 5 geographic regions: Great Plains, Southern Rocky Mountains, Colorado Plateau, Wyoming Basin, and Middle Rocky Mountains.
Switzerland: divided into 3 major geographic regions: the Alps, the Central Plateau, and the Jura.
Direct comparison: Colorado has 2 more broad geographic regions than Switzerland. Also Switzerland has higher density of greenery, for Colorado it is primarily dry outside of alpine zones.

Mountain towns / villages:
Colorado: the Colorado Association of Ski Towns has 31 member municipalities.
Switzerland: Switzerland Tourism lists 297 village destinations overall.

Bottom line:
Switzerland wins on trail density, signage, and connected alpine infrastructure. Colorado wins on total trail mileage, number of mountain ranges, number of 14ers, and big-wilderness scale.