It's a difficult one.
I can see where Mchka is coming from. It would be easier, and cheaper, just to pack it in carboard. It would probably be sturdier, as well.
I've read of other people who just take their bikes without padding at all, the thinking being, like Machka said, that they are difficult to handle and as such don;t just get thrown onto a pile of luggage. I suspect there's perhaps a bit more respect (or more chance of being seen purposely damaging the bike, as I'm sure is sometimes the way).
I can see the benefits of all systems really. The hard case is the best option if you've got somewhere to leave it, and so long as the case doesn;t take the weight over the limit. The bag is good for storage when there (even if there's no storage at the airport - if there's a nearby station), and taking into hotels.
Boxes are good in that they are cheap, but where to get a new one? You could ride to the nearest bike shop, but then you have to get boxed bike back to the airport.
I can tell I'm going to have to think about this.
The only deciding factors so far are that if my friend and I fly to Stuttgart, the airline stipulates some covering (bag or box), as does the hotel on our first night. So just bare bike is out of the question.