It is really difficult to generalize. Some of the designs were the same, but after WW2 the Zeiss Jena production facilities were decimated by the Russians. The Western company had to start from scratch. Both companies had optics made in other factories in both the GDR and West Germany. In the early period after WW2 Carl Zeiss lenses from west Germany were not necessarily made by Carl Zeiss. Much later on the 'Jena' label became something of a trademark that was stuck onto things that were not necessarily made in Carl Zeiss Jena. Similarly, some optics from CZ west Germany were made... 'elsewhere'.
Bottom line is all CZ optics are good designs, usually they had good quality control. West Germany quality control was usually better than the later period in the GDR, but you pay for it. But even GDR QC was usually much better than the Ukranian or Russian lenses.
As for grease... the communists seem to have a problem with lubricants! My Sonnar was a bit loose and sloppy. I sent it to a German technician for servicing and it came back silky smooth and tight.