Four days Nature in Japan: Aso vs Hakone

Dear Japan Gurus

We will be in Japan this Fall, travelling with friends. But we arrive some days earlier (Sept.27) and only meet them on Saturday (Oct.1) in Osaka. I first wanted to go to Aso in the days in between, but now I wonder if it maybe is too much traveling and it maybe would be better to stay in the Hakone region and the Japanese Alps.
Aso would probably be more special to us (from Switzerland) but if it's too far I rather have more outdoor time, possibly climbing Mt.Fuji.
Does someone have advice on what is more worthwhile to do in four days?

They are two completely different areas offering two completely different experiences.

Not sure how you relate Aso to Switzerland. But if you cannot decide. Then just go the one you mostly wanna see.

You wont require 4 days in either region. So you'll have time to travel to Osaka without being rushed.

Have you thought about Kamikouchi? It is really pretty there especially if you stay overnight, the food is awesome, and there are heaps of trails some of which are quite advanced. I'd take it over Hakone (which I liked, just not as much). If you look at it, check out the Onsen Hotel which I stayed at for 3 nights. It is brilliant.

A nice little run would be Tokyo - Matsumoto (check castle) - Kamikouchi for a night or two - Takayama - Osaka.