I do not have this dilemma since I do not have a 70-200

But I genuinely love hiking with the 100-500. It's the perfect lens for Alpine mountains, assuming you're ok with panoramas....
Weight is about right for me, IQ and AF speed are great and I like that it doubles up as almost-macro as needed.
All the mountains / skiing images here were taken with the 100-500
Shameless self-plug