Is it safe to just change the permissions on the bitcoin and armory directory to 666?
It would most probably fix your problem but isn't recommended.
Or is there a way to change the owner of the file on the Mac so the Ubuntu user can set it to what ever it needs to be? And what should it be?
Are you only accessing these files/folders from your ubuntu machine from now on?
If so, you are free to change the owner to your current ubuntu owner:
sudo chown -R USER FOLDER
Replace
USER with your user and
FOLDER with the folder containing all other folders and files.