"Airline approved", = lockable hardcase and for bows, it dosn't even need to be locked.
The best way all around is to use the takedown softcase and pack it in the middle of your gearbag with clothing all around. I put my arrow cases at the bottom and the bow on top of them with padding on all sides. I use heavy hunting socks to put the riser and limbs in. My stuff has been all over the world on many trips with no problems this way. If I travel to a foreign country, I check out their customs regulations for archery equipment and print it out(most have no special regulations), some customs officers will ask for your "permit", I just had the print out and look them right in the eye and say "I don't need one, they are available or required", they always try to get rid of me fast!