<<"I had almost finalized everything but I realized that if I shift my basefrom Wengen to Murren I can save CHF 400 on my hotel that I can use onsomething else.
4 star Sunstar Alpine Hotel in Wengen is CHF 1060 for 4 nights.
3 Star Bellevue in Murren in CHF 660 for 4 nights. ">>
I do not know anything about either hotel.
I do know that, in the ranking system of the Swiss Hotel Federation, the number of stars indicates the type of amenities, not the cleanliness of the hotel. More stars, more amenities - such as swimming pool, sauna, features/ furniture in the rooms ( a desk or writing table, for example.), reception staffed for longer hours, etc..
Although I am not suggesting that a swimming pool is the difference, there will some facilities or amenities at a 4 star hotel that are not present at a 3 star hotel. You might consider that a kind of hidden "cost" to use the term very very loosely.
Here is more than you ever wanted to know about the Star ratings of Hotels in Switzerland
www.hotelleriesuisse.c h/files/pdf8/Kriterie nkatalog_Normen_2015_2 020_CH_en1.pdf
I am quite comfortable staying in 2 star and 3 star hotels, but will sometimes go higher if there is a special restaurant, special views, or preferred location. Then I pay more.
Some of your planned hikes may take a few more minutes to reach them from Mürren than from Wengen; others may be easier from Mürren. The differences are not significant, in my opinion, except for access to or from Männlichen. That is easy from Wengen, but requires some more travel from Mürren. And, on the othr hand, obviously, a hike starting in Mürren is further from Wengen. ;-)