I have both the sandwich type (Trico) and the suitcase one (TC-1).

After a while the TC-1 hinges don't line up and when you close it, it squishes the bike outwards. You can never seem to get it right. Also, the locking mechanisms get banged up by the airline handlers.

Whereas, on the Trico, you align everything and then slowly tighten each strap. Everything is prefectly lined up, no movement away from the hinged area because there are no hinges, no little buckles and little parts to break.