One of the differences would be be the GC not having a federal army - at least not before 1871 IOTL.
Well, if the individual states are still "going it alone" militarily, they have no more chance of resisting Austria than they had OTL of resisting Prussia. In 1866 just one Prussian army out of four was able to mop them up. So with Prussia defeated and out of the game, Austria can certainly dominate them.
So the only alternative to accepting Austrian ascendancy would be to become protectorates of France - a sort of revived Confederation of the Rhine. But even if Nappy III was interested, 90% of Germans would see this as a cure worse than the disease. If they have to be dominated by somebody, well at least Franz Josef is a fellow German. If he was the lesser evil than the King of Prussia he is even more of a lesser evil than the Emperor of the French.
Your examples below give the answer: Until the next major crisis, external or internal. But since crisis do happen from time to time, the TTL Austria is as doomed to failure as OTL's Czarist empire and Sowjet union were. They were lucky to reinstall their imperialsim in thransition between the two.
Ok so they may possibly have some sort of crisis fifty or a hundred years hence - but then again they may not. anyway it isn't an immediate problem as Hungary is currently powerless to rebel in any serious way.
Russia has more inherent stability due to its size and raw materials and a better defensible border, more Russians than Austria has (German-)Austrians, .
And Hungary is also less homogenous than Poland or even Ukraine. If the Magyars rebel, the Croats are likely support the Emperor, etc. He wouldn't face anything like a united opposition.