Faldage, citing authority claims
barbaric doesn't seem to carry the connotation of cruelty that barbarous does.

NicholasW, citing perhaps common sense, claims
'Barbarous' has the sense of uncouth, foreign, or uncivilized.

'Barbaric' has the sense of cruel, horrifying, or "mediaeval".

Now that you are suitably edified, welcome to the club. We are, AnnaS should forgive me for saying, anything you like except unanimous.