An ok example but then again in the warring state period the chinise did ok against the nomadsSince China is mentioned however, I would just say that China is another monumental example of why centralization is not really an effective thing in the pre-modern world.During the Spring and Autumn period and the Warring states period when the country was feudal, it had no problems beating nomads despite being divided into multiple states. By the time the country was united however,it has tremendous difficulty fighting nomads whenever there was a long time of peace within the interior. The reason was surprisingly similar when you look at parallels with the ERE. The landlords usually just gobbles land reserved for the military and did not invest the resources they gained from them on their own military forces. This forced the various Chinese empires to spend significantly more resources on fairly unreliable and corruption prone regular militaries which, when failed, exposes the interior of the country to invasion--with nothing to stop them except natural barriers along the Huai River and the Qin mountains where the Chinese regimes could regroup and rebuild a capable military force to stop foreign invasion.
But then again the zhou kicked the nomads out ,
Also the( Di Cosmo 1999, 892–893 & 964 ) it was the qi empire that kicked out also many nomads and heck forced the nomads to become more united and was part of the formation of the xiongnu Confederacy.
there is also the case of the han destroying the xiongnu empire in fact china is in my opinion not solid proof sure in divided times some parts of china could deal with the barberians ( not always as seen by chingis attacking a disunited china and destroying the tangut kingdom and the jin or the case .
and also that the nomadic tribes would do damage to mostly when a dynasty was new or doing bad but then again the success of the zhou han and tang undermine this sure some of them had more difficultly than others but then destroyed the tribes .
heck a good comparison would be the hre in the late 10th century having no problem dealing with minor incursions and bearing the arabs and bulgarians back and conquering them .
But the comparison with china does have it's problems there were many reasons why period in chinese dynasties that led to the rot of the army
Which almost had to with politics in fact
In one of them been the tang giving the Jeidushi to much power caused a massive diaster as they were tied to the court to have loyalty but this was not the case do to li linfu and you had an lushan
Also the Jeidushi become defacto hereditary and did more to undermine the tang recovery post a lushan rather than defend which they failed to as seen by the tibetan attacks .
Corruption of what you mentioned of the central state was a part and heck china had some cultural things later on that made the military even weaker ( but these don't apply for the byzantine) but the Jeidushi are enough proof that a divided china is not always better .