If it's a minor victory, eg. the Russians successfully defend their lands and push the British and the French from the Crimea but can't contest them much beyond them, then the Russians could really only demand diplomatic concessions. These could include, the demilitarisation of the Black Sea for the Ottomans, the formal independence of the United Principalities, trade concessions, reparations, and the religious concessions the war was nominally fought over. Britain and France would look weak, while Russia would look strong.
With Napoleon III's empire reliant on continued success, the Second French Empire might be overthrown or at least given the opportunity to reform away from it's absolutist tendencies.
With a weakened France, and a untriumphant Sardinia-Piedmont, Italian unification is pushed back, although I believe the cogs were already moving on that so it's only delayed, not defeated.
Palmerston, I suspect would survive as PM of Great Britain under a minor defeat, but with reduced political power in the parliament. There may be a greater drive to demonstrate British power colonially, especially in India and China.
More generally for the Concert of Europe, The Ottomans decline would almost definitely be set in stone, and the Eastern question would begin to dominate the concerns of most powers, especially Austria-Hungary who most feared becoming the next sick man of Europe. With a triumphant Russia riding a wave of Pan-Orthodoxy, Austria-Hungary, already having dishonored it's alliance with Russia may start to reconsolidate against the Russian Empire and the threat it meant to the survival of the Dual Monarchy.
If instead it's a Major victory for Russia, that they are able to push into the Ottoman territory, then it's a slightly different story. A Peace in this context could lead to an independent Bulgaria, and an independent Romania (although without Southern Bessarabia). Greater Caucusus land could have been taken from the Ottomans maybe even up to Armenia if the Russians desire it.
Most importantly, a major victory almost guarentees Russian control of the Turkish Straits, whther by annexation or by diplomatic imposition.
Everything which happens to the defeated powers happens as in the minor victory except that I can't see the French Empire or Palmerston's government surviving a major defeat to the Bear.