AFAIK once there is a global warming chain reaction it may well be the end of all forests, the Amazon including and the end of most agriculture.

I can see how the tropical forests may become tropical deserts, but I don't see why now-frozen huge territories in Canada and Siberia won't become available for agriculture as temperatures rise.

What are we going to eat afterwards?

Worst case scenario: We can devour the flesh of 90% of humanity, and we'd still be 9% better than in the thermonuclear war scenario you mentioned.

I'm not claiming that 1 would be better, I'm just questioning the reasoning choosing 2 over 1 without providing the burden of proof.

When scenario 1 begins with the death of 99% of humanity, and scenario 2 does not begin with any deaths, I think the burden of proof is on you to explain how the hypothetical dangers of scenario 2 could possibly be worse than the given deaths of scenario 1...