Has Clausewitz's Western philosophy of war proven superior to Sun Tzu's Eastern philosophy of war?

You can not really make that argument that Clausewitz > Sun Tzu, because, seriously, when have the two concepts really been in direct competition in a war? I can not think of any instance.
What you can do is compare the use of strategy and cutting edge technology to the use of brute force and large numbers.
Germany was the former, revolutionary strategies, Blitzkrieg, combined arms, radio communications on the battlefield, and high tech tanks and combat aeroplanes.
That worked great against the large-numbers enemy France. They got steamrolled by the Germans. It worked great at first against the brute force, huge numbers Russians. But at one point, Russian numbers, together with the harsh weather, became superior to Germany’s superior technology. Eventually Germany lost most of their forces in the Russian Zerg Rush, making it easy for the western allies to defeat the remnants.

Actually, I can think of some instances where Sun Tzu, according to what you wrote he was about, was used successfully by the west. For example when the US secretly supplied the mujahedeen with modern weapons and training and helped them drive them out of Afghanistan.
Or when the US secretly staged a coup to remove the democratically elected government of Prime Minister Mohammed Mossadegh in Iran in 1952 and install a dictatorship instead.
Or when they helped stage a coup in Chile to remove the democratically elected socialist Salvador Allende, leading to a dictatorship under Pinochet.

Agree, it’s a bit of an oversimplification to say Western hegemony = superiority of Vom Kriege over Sun Tze’s Art of War.

Clausewitz’ strategy empircally failed twice for the Germans, if that means anything.

No, it’s not meaningful to make such an overt comparison, though the question can spark lots of conjecture and thinking about strategy and philosophy.

To which end, I’d broaden the idea to point out that Sun Tzu has wider applications outside literal warfare, and is studied and applied by non-warriors, I would say to a far greater degree than von Clausewitz is.

And if economy has become an axis of modern conflict between nations, Sun Tzu has much broader application and relevance than von Clausewitz.

Successful applications of The Art of War are generally much less obvious than applications of Vom Kiege. The best success may be one where the opponent doesn’t even realize there has been the potential for a conflict.

I see no exclusivity between them. They can be used in tandem.

@Zaku GA

Personally, I see The Art of War as superior, but that is just my opinion; like others have said, the comparison isn’t really as simple as that.

small point for TAOW: Japan may have lost militarily, but Japan essentially controls the west coast of the U.S., economically; and have one of the strongest economies in the world, in no small part due to TAOW-esque methodology. Same goes for China. Our U.S. economy is actually fairly dependant upon major asian powers. In other words, the non-military applications of TAOW are making bank for the east.