Why were the Austro-Prussian War of 1866-7 and the Franco-Prussian War of 1870-1 relatively short war?

The Austro-Prussian War, which has also been called The Seven Week War and one of the Wars of German Unification, and the Austro-Prussian War were short wars ostensibly because Otto von Bismarck, (who was appointed premier of Prussia in 1862 by William I the Prussian King) had been planning these wars for some time, in fact he had manipulated the Austrians after the Danish-Prussian War. Using the Schleswig-Holstein, former Danish territory that was annexed by Prussia and Austria after their defeat of the Danes in 1864. By the Gastein Convention of 1865 the two countries agreed to rule jointly, Prussia was to administer Schleswig and Austria was to administer Holstein but disagreement soon developed. When Austria brought the dispute before the German diet and also decided to convene the Holstein diet, Prussia declared that the Gastein Convention had in this manner been voided, triggering the Austro-Prussian War. Just as Bismarck had planned at least as far back as 1862, he had told Benj...