To start with you should decide what trails you enjoy and what type of riding you want to focus on. I would not build a bike for downhill once or twice a year that you will otherwise ride on singletrack. The three frames you listed all fit different categories, with a little overlap on the 936/909.
AM831: all mountain, 150mm travel, should be great on descents but still climb alright
FM936: 'down country', 120mm travel, aggressive cross country and light trail
FM909: modern cross country but still 100mm travel, likely fastest on singletrack
Personally I'm on the FM936 b/c the terrain here is relatively flat with occasional elevation and it works great for all of it. I've ridden this bike in CO and UT, including the Whole Enchilada, and survived but those areas would be better with more travel. If I lived in the mountains I would definitely consider the AM831.