Russian elite of 1876 has VERY unpleasant memories of a war against a European power (or coalition thereof), wounds of Sevastopol are still fresh. It is unlikely that they would risk "Crimean war 2.0". So, would Austrians firmly object, Russians would not cross Danube.
Would Austria's fairly quiet but firm rejection of Russian intervention, followed by an Ottoman crushing of rebellions and Serbo-Montenegrin intervention, or an Austrian imposed compromise been very offensive to Russian opinion and created a nationalistic rage as severe as Russian rage against Vienna, and Berlin, after the two powers supported or brokered the revision of the San Stefano treaty?
One thing is that without the Ottoman-Turkish war, Russia does not recover southern Bessarabia from Moldova and restore its pre-Crimean War border. Was this a bitter Alsace-Lorraine type issue for the Russians?
Unless the Russian reaction to Austrian objections would have been a commitment by Russia to a war of revenge on Austria within a generation or so, we can say Vienna fumbled in aiding/abetting/going along with Russia's initial plans to intervene, especially considering that Austria-Hungary (especially Hungary) had nearly equal misgivings about annexing additional Balkan slavs to the dual monarchy, or having them fall under Russian influence.
If the wounds of the Crimean War were still fresh, I guess Austria wasn't exactly stellar either. Austria had lost its previous wars against France and Prussia over the previous twenty years as well.
Russia would probably focus on continuing to develop its military or maybe focus on the Far East instead. Maybe we could see the Russians begin their Trans-Continental Railway earlier (not saying 1870s, but maybe the 1880s or 90s). It would be very interesting.
Perhaps, if the Franco-Chinese war of the 1880s unfolded on schedule, the Russians might have joined the French side to seize one or more of Xinjiang, Mongolia or Manchuria?
Also it would be interesting to see how the Balkans unfolds. Maybe later on Austria will be the region's main aggressor?
I'm not sure what the Austrians would have done. What they probably should have done was just support the territorial status quo, because for the most part, they did not want to add more slavs to their state, but they did not want increased Russian influence in the area. The logical third choice if those are undesired is perpetuation of Ottoman control.
But I doubt the Ottomans could retain the Balkans.
I guess because we would just expect continued rebellions. In military terms, at the time the Ottomans were capable of suppressing any given rebellion and defeating Serb and Montenegrin armies that intervened.