Sep 19, 2016 - 3:03 PM
The Swiss Travel Pass does not cover the La Braye lift, but you may not need that as I assume you'll buy a ski pass that includes it. It does include the Alimentarium. The Regional Pass Lake Geneva - Alps does not include the Alimentarium and gets you a discount to La Braye.
Both passes are somewhat problematic for the 10 days you spend there: the Swiss Travel Pass is available for 8 or 15 days. The 15 day pass would still be worth it as a regular ticket from the airport to Château-d'Oex and back costs more then the price difference between an 8- and 15-day pass.
The Regional Pass Lake Geneva - Alps only comes as a 5 or 7 day pass with only 2 or 3 days of free traveling. I'm afraid that's too limited because you intend to travel every day. I am not aware of a promotion by the way.
The Swiss Travel Pass will definitely be more convenient. And you can print it at home, so no shipping costs or waiting for a ticket office to buy it. Price wise, you will have to do the math to be sure.
Further details are here (maps, where to buy, how it works):