Hi and a very warm welcome.
Personal preference, really. And it can come down to how user friendly the hard case may be as regards getting it in and out of the car. Hard cases might, ultimately, provide better protection, but are less wieldy.
I have never had to transport a rifle abroad, but especially if you were flying, the hard case would give more reassurance. And (total guess here) may be a requirement anyway.
A good (and great value for money) compromise is the BSA Polytwill "bag". I have one, it being recommended by a BBS member. Excellent. But even that, with it being of stiff, sturdy construction, is a little less wieldy than a traditional padded slip.
For field use, I'd definitely favour a padded, less rigid slip.
Hope this helps a little.