Charlotte
Once the flowers have completely hardened it really does not make a difference which type of box you keep them in. I use both methods.
Now I believe I read if you were going to put them in the fridge after they hardened you want to only use the cardboard box and then put that box in plastic. It supposedly helps with the condensation.
Also I think some people use the air tight containers to put not fully hardened flowers in to help keep them soft.
Hopefully I helped a little bit :)