Barbarian, barbaric, barbarous, savage are comparable when applying to people or characteristics of people that are not fully civilized.
Barbarian frequently applies to a state about midway between full civilization and tribal savagery.
Barbaric and barbarous may also be used to express this notion.
Savage implies an even less advanced and more primitive state.
Barbarous and savage are somewhat more commonly used than barbaric and barbarian to indicate uncivilized cruelty, but all may be so used.
Barbaric and barbarous are more common in relation to taste and refinement.
Barbaric suggests a wild, profuse lack of restraint.
Barbarous implies an utter lack of cultivated taste and refinement.