To all three of you;

I would stick with the Rimowa "IATA" model. The larger (56cm) model is over the limits for UA, for Air Canada and for Lufthansa. Sure you might "get away with it" but you will likely be challenged.

Remember that all these airlines also have a strict weight limit, and the larger case will be easier to over-pack.

The only airline I know (there may be others) which will accept the larger case is British Airways.