For packing, there are dozens of you tube videos. Some are not very good and do not provide a lot of protection and some are probably more work than necessary, but if you look at half a dozen of them you will get a pretty good idea of what is important and what is not.
Regarding your specific question, bike case or card board box, I suspect it is somewhat dependent on your budget. And of course, the quality of the bike box if you got a used cardboard box from a bike shop. And the weight of your bike since a hard case often is somewhat heavy which could trip an airline weight limit if your bike was also on the heavy side.
I am not saying these are the best videos, but since they were produced by a shipping company, they have some automatic credibility.
https://www.bikeflights.com/pack
I have only flown with my S&S bike and with my folding bike in an S&S case, not with a conventional bike which I assume you have. Thus, I do not have much other advice to offer.