Those hard boxes have two problems. They are expensive and they are heavy. But they are wonderful. You are almost certain that your bike will arrive in one piece.
To use one or not is going to depend on the airlines. Some aren't real picky about the weight others are. You should also check the dimensions of the case. Some are within Fedex / UPS limits others aren't. Mine is not but then again I only paid $60 used and it has already paid for itself.
But the advantage of cardboard is that you can just toss it at your destination as others have said.