IMO, the Germans were ahead of the curve, if only out of necessity; being pounded day and night by the strategic air forces of the US and Britain (respectively) makes you concentrate on how to most effectively destroy aircraft. It reminds me of the phrase that Samuel Johnson (supposedly) uttered the night before he was to be hanged: "Depend upon it, Sir, when a man knows he is to be hanged in a fortnight, it concentrates his mind wonderfully."
However, we must also remember that the two Air Forces (Allied & Axis) had, essentially, different missions, especially during the latter half of the War; the Allies were primarily concerned with destroying smaller and faster fighters, hence their predominate use of faster-firing but smaller-calibre weapons, whereas the Axis was more concerned with destroying much larger and heavily-armored bombers, hence their prediliction towards larger but slower-firing cannon.
As the website points out, however, it is the obvious superiority of a multi-chambered (if not multi-barrelled) weapon, like the MG213C, that presaged modern fighter weapons; if the Germans had been able to field the MG213 any earlier, there would've been a lot more Allied bombers shot down.
P.S. A little off-topic, but the same website has an EXCELLENT discussion of the assault rifle ammunition controversy:
ASSAULT RIFLES AND THEIR AMMUNITION: