I would not think either would do much better for keeping water cooler.

I bought neoprene "jackets" for our Sigg bottles and they really do work.

Slipping a Kleen Kanteen in a thick wool sock would work too. I use this trick on any water I carry in my pack. The slimmer metal bottles slip into a sock way easier than the plastic.

Back when I climbed I wrapped my Nalgene bottle with closed cell foam.....more to keep it from freezing than to keep the contents cold but, other than pretty ugly, that worked great.