boxed.

i use a neil pryde designed bike BAG regularly and have had no problems with it, these are much cheaper than boxes.......normal price is about £100 but if you shop about you can get them for about £60...they come with various brandings (e.g Tifosi, Evans, etc) but are the same bag

I've used cardboard boxes for trips to Nepal, Auz, NZ, Morocco, Spain

The key is to pack them properly and tape up the box really well. I use parcel tape and plenty of it. I also fit a strap so I can carry it like a big laptop - helps when legging it through airports

A dedicated box is obviously better but more money. The cardboard one also has the option to discard it at the airport when you arrive. Handy if you're flying into one airport, then out of a different one.

We did this in Spain - flew into Malaga, but out of Madrid. Picked up another box in Madrid from Decathlon store (I think) for the flight home.

I too use a bag rather than a hard case/box. It's a large padded bag from Planet X and seems to work fine - it's been abroad (to Switzerland and back) four times this years and to Italy and back once this year. I remove the wheels and drop them into the wheel bags which are integral to the bag. I use a bit of thin hard board to cover the outside facing side of each wheel so they cant be crushed. I wrap the bike in bubble wrap, taking care to wrap the derallieurs, STIs and chain rings well, then put the whole thing in as it is, then turn the handle bar/fork steerer fully round so that the forks are less likely to be crushed together as they are facing length ways rather than across the bag. I then undo the clamp bolts on the stem/handle bar and turn the bar under so that the drops/bar ends are facing upwards - so the STI levers are not sticking out. I don't even need to put my seatpost/saddle down. You don't need to totally deflate your tyres though they may ask you if you have. Just knock a few psi out and they will be fine. I put all my cycling kit, shoes and tools etc into the bike bag as well because it's huge and I might as well fill the space and then I only need take hand luggage on most trips.

IME bike boxes are too heavy and so baggage handlers don't like them - just dropping them out of the hold onto the tarmac! I watched about 20 coming out of a plane hold and dropping about 10 foot onto the tarmac at Toulouse. The bagged bikes were lifted onto the conveyor - so make sure you don't pack your bag too heavy - if it's over 15kg it gets marked 'heavy' and needs to be tough. I bought a rigid bike box a few years ago and it was trashed on the first trip and so I've used a padded bag ever since. Worth getting the plastic spacers for the fork/rear ends from your LBS too - pipe lagging and cable ties does the rest. Unscrew the rear mech and cable tie to the rear frame spacer to prevent your gear hanger getting bent too.