The choice depends on a few factors. The biggest is how well can you deal with the case when you are traveling. If you always fly to and from the same location and travel frequently enough to justify the cost a hard case is probably a slam dunk.

If you will fly into one place travel some considerable distance and fly home from another a hard case suddenly becomes a huge problem. This will often be the case for many tourists, but may not be for you.

A cardboard box works fine as long as you pack the bike sensibly.

A soft case is kind of a middle ground since it could possibly be carried along on the bike or more likely be mailed ahead.