As you said, you can say 大きいほうが小さい(の)よりいい, but 大きいほう means "something bigger", so I think it's noun (or noun-like usage).
You can say 汚いよりきれいなほうがいい. It also means something clean is better than something dirty or being clean is better than being dirty. I think "something clean" and "being clean" are noun.