I've done both. I have a hard shell bike case but now I almost exclusively fly with the bike in a cardboard box because:

• Most of my trips begin and end at separate airports and I don't want to hassle with shipping the case to my return airport. I make prior arrangements to have my bike packed by a local bike shop at the end of my tour. That way I know a bike box will be available even if I end up packing it myself. I request that they not seal the box because a) I want to check and make sure it's my bike and only my bike in the box. Some of the European airports still ask if I packed my own luggage. I want to be able to truthfully respond yes. And b) I want to put in the box some of my tools and other pointy things that I can't take on the plane.
• I also prefer the cardboard box because it is lighter than the bike case. One airline tried to charge me double bike fee because the hard shell case with bike exceeded standard luggage weight requirements, even though it fell within the specific fee for special luggage category.