I love B16’s cross. Is it Greek in origin?
I don't know. The East does use similar crosses, but that is a Church tradition to be found in both the East and the West. Both Churches also use simple crosses, and Russians have a simple, tripple cross, which many Orthodox churches use as well.
+Benedict XVI is a patristic pope. He sees the Church, and rightfully so, as an unbroken tradition that can never be "outdated" and therefore everything the Churhc produced is always "valid," and "current," just like the catholic and orthodox faith that was believed everywhere and always.