FF would give the AH empire its best chance of survival. The only unresolved issue would be the Czechs, which would be that much more frustrated now that all the other Slavs are taken care of (Poles have free reign in Galicia and Southern Slavs have their crown). The Hungarian nobility would riot and a surprisingly large number of the peasantry would support them. However, as a minority in their own country and the Southern Slavs now with a vested interest in the Austrians succeeding, the civil war/revolt is not likely to lead anywhere. And the outside powers (minus Serbia, who really doesn't count) are going to want to support stability in the region, especially Germany, but also Russia, as the Slavs are being given much more independence in the Austrian system. The Romanians might actually join in on suppressing the Hungarians too, as they were allied with the Austrians and probably are hoping for a reward for their help.
As to the Serbs starting a war over the issue, well, there is too much to go into that I don't have the time nor will to plow through. Mainly the argument against it hinges on the Serbian army's own calculations of not being ready for a war for 10 years, because of their ammunition shortage thanks to the war they literally just finished fighting, not to mention that they are still absorbing their rebellious new territories. Also the post-facto knowledge of Serbian fighting skill was not known at the time and a major surprise to everyone, including the Serbs. If they pick the fight by declaring war, they are not going to do nearly as well, as the Russians cannot support them without losing out diplomatically.
Now, as for the AH-S empire...they are not going to be in the fittest fiddle, but the Army is going to get a major boost. FF is primarily interested in expanding and modernizing the military (he was the inspector general after all and instrumental in getting Conrad into power-who was a fine reformer, though less than adequate as a field commander). The Habsburg empire will be much more managable, though not in all situations. Decentralization will be the name of the game, but with a much more middle class centered Hungary. War might not happen at all, but I doubt the Habsburgs could or would ditch Germany. They were too dependent on the Germans for economic and trade reasons to abandon their treaties. Italy would switch camps shortly, which changes Germany's calculations on things significantly and make their starting of any general war in Europe unthinkable.
I would be very curious to see how Russia ends up ITTL. They might not make it through Nicholas' reign without another major insurrection.