Define a big knife. 4 inch? 5 inch? 6 inch blade? What is big and what is small.
But for me, I have one 4 inch fixed blade made from Elmax, and for this kind of size, I dont want carbon steel. Elmax doesnt rust, it holds a great edge, it looks like it is tough enough for my needs. Hard to sharpen? Same old story over and over again, use proper sharpening equipment and it is quite easy to sharpen.
Over like 4,5 inches, that is another story, carbon steel could be better (toughness and so on), but again, you can get some nice tool steel that are tough and they will hold edge longer then pure carbon steels.