As long as you have same version on both, i.e. v.6, then copying over the .walletx (v.5) or .enpassbackup (v.6) should be what you need. Of course if you are syncing to a cloud service theoretically you should be able to restore straight from there.
As for your OS the officially tested versions of Linux are CentOS 7, Fedora 27 and Ubuntu 14.04 or later (64-bit only) as detailed:
I am running Xubuntu with no issues.