I'm looking to travel by train from Lucerne to Montreux in Switzerland.
sbb.ch gives me two main options:
Is the latter significantly more scenic? If not, I will choose the faster route.
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Yes, it is. Lake Neuchâtel is lovely and you can see it and the vineyards from the train. The line from Bern is just regular Swiss countryside, which is nice enough, and with a bit of luck you might be able to see the Berner Alpen at a distance, but I still think that from the two you listed, Neuchâtel is a clear winner.
The Golden Pass is a train route that starts in Lucerne. Along the way to Montreux you'll see the Brünig Pass, the lakes of the Bernese Oberland, the Simmen valley, upper class Gstaad and Lake Geneva.