I have bikes in my current stable with the different configurations:
S&S Coupled
Ritchey Breakaway
Bike Friday
Foldable
When I traveled overseas with my bike, I decided to go with AirCaddy, it requires minimum dis-assembly if any and personally I felt it provides maximum protection as in, hand it off to the airline luggage handler and forget about it.
I did paid for oversize luggage when we flew on United. But when we flew with Qantas, it was free. There's something nice about the Aussies, they seem to appreciate bikers a little bit more.
Technically speaking, I could have saved some money by breaking my bike down and using the intended case that meets the airline restrictions.
But in the end, I made a judgement call based on time, money, logistics, portability, safety (bike protection) etc.
I know...i always thought it's a bit weird to see people who has a break down bike and not use the "breakdown" function.
But so much of that decision is circumstantial. Every one of those trips that we took, we honestly thought that we would be staying put in our new place for good and so I want to make sure that my dedicated bike get to its destination in one piece and in flawless condition. To me, the Air Caddy solution seems to fit the bill. The other alternatives involving bike cases seems to me always involve some degree of risk and unpredictability.
I may be wrong in that I may be giving Air Caddy too much credit or placing too faith on it but that's how it went down - three separate overseas trips using the exact same box, zero issue, not a scratch, and it was a breeze putting the bike back together....put on the front wheel, raise the seat post, flip up the handlebar, tighten the stem front plate bolt, pump up the tires - and off we go.
The ONLY issue I have with this approach is ...the Air Caddy box is HUGE and it takes up space in the car, make sure you pre-arrange the proper transportation when you get to your destination.