I have used bags mostly and a box once and most recently I could only find sheets of plastic, tape and sheets of bubble wrap so I constructed my own bag.
Shortly after receiving my immaculate new touring bike in England (In a well-packed box) I flew back to Canada with the bike in a clear plastic bag. The baggage handlers either at Gatwick airport in the UK or Vancouver international in Canada dented the top tube and the airline refused to pay for the repair because they said while a bag is accepted as sufficient for transport it is not deemed properly protected and so they accept no responsibility for the negligence.
So now I have a new dented touring bike which, fortunately, has held up with little more than surface rust.
I've since flown twice, once with a cardboard box and once with he aforementioned sheets of plastic/bubble wrap.
The box was a stressful ordeal, I ad to hunt one down the day before the flight and almost couldn't find one at all. The next day I had to ride to the airport at 2 am with the giant box under one arm in the rain and heavy winds. When I got to the airport it took hours to disassemble and box the bike and then, because the box is not see-through, security took it all out again once inside the terminal and it all had to be repacked in in a rush. The box was wet and weak at this point but I made it safely to Bogota with no damage.
One month later I flew out of Santa Marta Colombia with the bike plastic and bubble wrapped and it was treated fairly well..no damage but the big chainwheel cut the plastic so next time I'll cover it with a piece of cardboard.
Bottom line is you can't guarantee anything. Boxes are often a logistical nightmare unless you are starting and ending at the same location and can store your box somewhere. If you're like me and have a bike bigger than most people good luck finding a box that fits in most of the third world or even Europe. I could barely find one in Canada and people there are relatively large.
In the future I will use my plastic sheet/bubble wrap and tape method because it offered the best of both worlds. It's still clearly a bicycle but it's padded a bit so it's less likely to suffer. If I were really clever I could incorporate a derailleur protector into the process but I think it's probably fine. I've flown with a bicycle five times now and 4 out of 5 times were with a bag or similar and only one time was there damage. Take from that what you will I guess.
It's also worthy of mention that with a bag or bubble wrap you can pick up the necessary materials days in advance (shop at your leisure) and carry them with you whereas with a cardboard box you can't really go anywhere with it, you have to store it somewhere or transport it so it's nowhere near as convenient IMO.