>> Are they both the same when it comes down to use in extreme cold conditions?
Eh well, that depends (of course).
Boiling pts:
Butane : -0.5 C
Propane: -42 C
Obvious operational difference here!
BUT for actual use with an inverted canister stove, it depends on how warm you kept the canister before use.
In my pack next to my water bottle, even when skiing, I KNOW the canister will be above 0 C, like the water in the bottle. (Both are against my back.) That works for dinner and morning tea.
I store my canister inside the foot of my quilt overnight in the snow, so it is above 0 C there too (like my toes). That works for breakfast.

When using my stove in the snow, I let a bit of the radiation from the flames reach the canister to keep it warm. Naturally, I monitor just how warm the canister gets. It dos not hurt to insulate the canister from the snow either, although I had not bothered here. Well, it was a fine sunny day, after all!
Cheers