The 5e Barbarian is weird. I personally think it should have been MORE offensive focused and less defensive focused. I find it a bit odd how tanky they made Barbs. I think the Barb should edge out the Fighter in DPR and the Fighter should edge out the Barb in defense, but the opposite is true.

Yes I think Rage damage should be slightly higher especially if Barbs are restricted to just 2 main attacks. Something mirroring proficiency bonus would be fine(tied to Barb levels of course)