Myself and my partner transported our road bikes with us from the UK, via Los Angeles, to NZ. These were transported in the hard bike cases and arrived intact (although they missed the flight and arrived the next morning, via courier). We simply had to turn the handlebars to fit them in the case.
Conversely, we also shipped out two hybrid commuting bikes, which were transported in the standard cardboard bike box - and sent air freight. They were packed very carefully by the shipping company, and wrapped in lots of bubble wrap, but one of the bikes still managed to sustain damage to the rear derailleur and had to be replaced.
The hard cases were worth their weight in gold and I'd only ever consider shipping a bike I love in them from now on.