A somewhat-frequent PoD bandied about when discussing an Austrian victory in the Austro-Prussian war of 1866 is the near-death experience of the Prussian king, Bismarck, and von Moltke with an Austrian cannon shell. Say that Austrian cannon shell had hit more precisely and the trio all died, causing chaos in the Prussian system, leading to an Austrian victory at Koniggratz/Sadowa.
Can Austria make any meaningful gains in the aftermath of this fluke victory? Or will the newly-crowned Frederick III of Prussia pursue more war with the side that killed his father? How will the occupied German states- Hanover, Hesse, Saxony, etc. fare in the world after the Prussian loss? What about internal developments in the Kingdom of Prussia? I have read on this site that there were sporadic revolts in Prussia that faded with the news of a Prussian victory. Would they get worse if Prussia lost, with king and prime minister dead so dramatically? And without losing 1866, would Austria have enough strength to prevent the formation of Austria-Hungary, the dual-monarchy?
Okay, let me try and break this down so I can answer these questions easily, or at least offer my interpretations:
1) Austria had lost its first clashes in Italy against Piedmont and France. In OTL, the Prussian victory at Sadowa forced the Austrians to cede Venetia NOT to Prussia or Piedmont (directly) but to France, which then gifted the territory to Piedmont. Should Austria manage to win at Sadowa, its likely that Piedmont might declare war on Austria again-possibly with French backing, and seize Venetia by force. Its even money as to how this war ends, but if Austria prevails, Piedmont might be forced to return Lombardy to them. It would be interesting to see a situation in which France and a smarting Prussia make common cause if only temporarily to join forces with Piedmont. (Given the tension between France and Prussia this is unlikely, but then we've seen France bury its hostility to Austria to check Prussia, so who knows? Prussia would almost certainly want revenge for its loss and France would be eager to reduce the power of the Austrians and potentially gain enough favor with Berlin to negotiate a revision of the Vienna Treaty of 1815).
2)I would expect nothing less than a Prussian return engagement under Frederick III, given that his father died at Sadowa. This is where I throw in the idea that in addition to Piedmont, Prussia might consider burying its hostility toward France temporarily and forge an anti-Hapsburg alliance. Russia could even be brought in either as an additional ally or as a replacement for France, as Russia would be looking for a way to neutralize the Hapsburgs so they'd have an open door to realizing their 'historic mission' in regard to Turkey and the Straits. Frederick III might be delayed, however, by any uprisings within the annexed lands of Hanover, Hesse and Saxony and would need to either reach an accomodation with the rebels or crush them militarily. Should he be successful in this, its likely that the next Prussian attack on Austria would guarantee that Prussian grenadiers would be just outside the walls of Vienna itself.
- Assuming on the other hand that Austria takes advantage of the surprise victory at Sadowa, or manages to coordinate with the German states that aligned with them more effectively (which would still allow an Austrian victory), I feel like Prussia would be partitioned. Saxony getting Berlin and Brandenburg, Hesse and Hanover getting some scraps of territory. The Rhineland could either be broken up among the middling German states or even constituted as a new kingdom (I highly doubt Austria would willingly give the Rhine Valley to France as they had just fought a war over Italy). Prussia would be reduced to its eastern territories and no longer factor as a German power. They might, in time, more closely align with Russia and down the line could either seek a new war, or join in a Russo-Austrian war to regain its lost lands.
3)Given that Austria would have increased its power with a victory at Sadowa, there is every reason to believe that the Hungarians would be quieted to such a degree that no compromise is ever made because one isn't necessary. But given Hungarian concerns about their culture becoming diluted with foreign influences, not to mention the very real threat of a major Slav state arising on their southern border, a more negotiated version of the Ausgleich could also still happen. I honestly believe it was Hungarian rather than Austrian fears of a Serbian superstate that drove the course of events leading to June 28, 1914. Would this change in the timeline mean the assassination still happens? Possibly, but its also possible that a more negotiated version of the Ausgleich could impose limitations on the Hungarians in terms of their behavior toward the non-Magyar inhabitants of their state. Better treatment of the Romanian and Slavic inhabitants would in time lead to less tension than in OTL, though in the end, Romanian irredentism and Serbian aspirations to empire would still trigger a Balkan Crisis. It would then depend on the alliance systems in place by that time as to whether the crisis remains confined, or spreads.
One Final thing to note: Should Sadowa be an Austrian victory, it stands to reason that Prussia would be temporarily prevented from continuing its mission to unify Germany. In addition to the other potential terms Austria could impose, the restoration of Schleswig-Holstein to Denmark isn't out of the question. Also, without a Prussian-unified Germany, there would be no conferences headed by Bismarck which decide the fate of peoples in both the Balkans and in Africa, and colonial conflicts between the major powers could easily erupt. The loss of Prussia as the driving force for unification could also, lastly, open the door to a Grossdeutschland under Austrian leadership which might even incorporate Hungary as an autonomous state. Austria could even possibly decide to shed its Italian connections to focus on Germany, though they'd hope to wean the new Italy from their French alliance.