In my own "a different 1866" TL, Prussia indeed ends up annexing the Sudetenland, but this occurs as the ultimate result of a rather different Austro-Prussian-Italian war, where Italy performs much better, winning decisive victories at Custoza and Lissa, which allows it to ask all its claims at the peace table. This pushes the rest of the Prussian elite to ask for all of Bohemia-Moravia (and Saxony) to keep the pace with their own allies, and Bismarck is simply overruled on this. Napoleon III intervenes and threatens war to moderate the Prussian-Italian demands. With most of their armies in the East, Berlin and Florence are reluctantly forced to comply, which ends up into Prussia getting Saxony and the Sudetenland (besides the OTL stuff) and Italy getting Trento and Gorizia-Gradisca (again besides the OTL stuff).
This however wins Austria only a temporary reprieve. Total defeat in the 1866 war, on top of the other 1859 defeat, sends the Habsburg empire on a death spiral. Overconfident France picks a fight with the Prussian-Italian alliance over the twin casus belli of Luxemburg and Rome in 1867, and gets its butt handed over on a place even more so than OTL as a result. Napoleon III is only able to woo Denmark into a most unwise revanchist alliance, which results into German annexation of Denmark. Austria almost does likewise, but it is getting too nstable and mobilization is called off at the last minute. A few years later, when the Russo-Turkish war is raging, Austria collapses after a last-ditch, half-hearted Ausgleich attempt fails, and the empire is wracked by rebellions by Magyar and Slav nationalists, German liberals, Pan-German nationalists, etc. Bismarck sees the writing on the wall and under pressure by German nationalists and his Italian allies accepts his destiny as the unifier of Grossdeutchsland.