As many have said, it's not just the material in general. Aluminum, Steel, Carbon. It's also about the particular alloy whether steel or aluminum, I presume Carbon has different blends too, but don't know for certain. As well, tempering of the materials, how the particular manufacturer handles, shapes and otherwise manufactures the part whether handlebars, frame or what have you.

So you just can't put a one size fit's all generalizations that heavier is better or worse.