I use both both it depends on what I am making. Hobbs 80/20 has a bit more thickeness to it but does not have the structure that the scrim in Warm and Natural has in it. So if I want a bit more "puff" and better drape its Hobbs 80/20. If its for table runners that I want to lay flatter and have that "structure" it Warm and Natural. W&N is easier to preshrink , important for table runners to lay flat .
There is a difference in the recomended quilting distance.. .those battings without a scrim typically require denser quilting.
Contrary to popular belief .. Warm and Natural is not 100 percent cotton. The scrim used is Poly, the fibers that are pushed through the scrim are 100 percent cotton. Last I checked the fine print on W&N there was 13 percent poly (the scrim) .
I have not put equal size battings on a scale , but it feels like the Hobbs 80/20 has a bit more weight.
Interesting, in my area finding Hobbs 80/20 is not so easy. Jo'Anns discontinued stocking it... and only one LQS has it and NEVER puts it on sale. So its an internet purchase for me.

The Warm company does make a cotton/poly blend but it is known as Warm Blend and it is 50%cotton / 50% polyester. And yes Warm & Natural has a scrim. In my experience, if you quilt densely, Warm & Natural becomes stiff and Hobbs 80/20 is less stiff.

While Warm and Natural feels much nicer BEFORE it's quilted, Hobbs 80/20 feels much nicer afterwards, in my opinion. Hobbs is also much easier to handle on a longarm.

I hand quilt and have used both but Hobbs is much easier to hand quilt.