I've flown all over with several of my Bike Fridays (NWT, Pocket Rocket/Pro, Air Glide) and several suitcases (Carlton, Oyster, Samsonite F'lite).

It really helps if you use the Bike Friday products that are designed to help protect the contents of the case in transport:

https://store.bikefriday.com/index.php?cPath=31

As to which suitcase, it also helps to not exceed the 62" maximum dimensions allowed for international travel without extra surcharge. My Carlton & Oyster cases are just under 62", while the F'lite exceeds by about an inch.

Never, ever, ever exceed the 50 lb. international weight limit for any single piece of luggage. Once you do, they'll sock you for overweight, then whip out the tape measure and check for oversize.