The American Civil War went on for four long years, took an immense toll on local populations, and ended in the deaths of more Americans than every other U.S. war combined. But if you look at the European wars of the mid/late-19th century — the Italian Wars of Independence (the first lasted one year, the others a matter of weeks), Schleswig War (less than a year), Austro-Prussian War (a few months), Franco-Prussian War (less than a year) — they were far briefer conflicts, whose result hinged on fewer battles. The Crimean War is an exception to this, and may be worth addressing in an answer. However, my question is this: Why did the American Civil War last so much longer than other conflicts of this period? My intuition tells me that it has something to do with the sheer size of the American South, and the choice of the Confederacy to simply avoid direct conflict with a superior foe, and prolong the conflict until the Union lost interest. But that isn't entirely true, as the Civil War had many large-scale battles, plenty of which were actually won by the Confederacy early on. Does it have something to do with a difference in technology, strategy or geography?
The reason for that disparity is the extent of peacetime planning for war in Europe compared to the U.S. as a result of different political values. France, Austria and Prussia/Germany all maintained standing armies and detailed mobilization schemes that allowed them to fight very hard at the outbreak of the war. This kind of thing was the norm in Europe with a few exceptions. However, it was unthinkable in U.S. politics. Indeed the "unthinkable" nature of the ACW also acted to prolong the war.
When the American Civil War broke out, each side could only throw a fraction of it's military strength into the fight. They started the war in April 1861, and had an important battle in July (First Manassas) which only a tiny fraction of the country's military capacity was employed, say, 35,000 men per side out of an eventual 800,000 peak strength. After that, each side tried desperately to recruit troops and throw them into the war. There was no pre-war conscription plan, but each side created one during wartime. The officer class of both sides was inadequate to staff a national military. Men with minimal military training and experience often lead regiments or larger formations. The ACW lasted for a long time because they had to build an army and fight a war at the same time. Eventually, of course, the South ran out of military resources before the North, but that took a very long time as each side trickled in men and money very gradually.
In contrast, countries on the European continent had detailed pre-war plans of how they would fight a war against their probable opponent. Win or lose, these plans were effective in throwing a large chunk of the nation's military capacity into a war very fast. In the Franco-Prussian war, the armies had important engagements within three weeks of the outbreak of the war, and fought the decisive battle at Sedan with 130,000 to 200,000 men (and that's just the armies on that battlefied) within two months of the outbreak of the war. This performance didn't happen by accident, each side had a military mobilization system that enabled it. Men and especially officers were trained in peacetime. A plan of who would be drafted from where already existed. Railroad plans were created to bring these called up soldiers to the front rapidly. How well this system worked when tested in battle varied by country and war, but every European state knew they might fight their neighbors and had well developed plans and infrastructure on how they would fight and they could see if those worked in a few months of fighting.
Obviously the political and geopolitical situation of the U.S. was very different from Europe. European governments knew they could expect to fight wars with their neighbors. The population generally did not resist various recruitment or conscription schemes. Whereas in the U.S. a longstanding political tradition disdained large standing armies and was opposed to the government planning to impose conscription in peacetime. With no large military powers in it's vicinity, the U.S. government and population alike felt it would not need to plan for a massive war. In the period of rising political tension before the ACW, little or no prewar planning could be done overtly without creating a spark that started the war.
Lastly, there were certain forces in the European balance of power system of the late 19th century that kept wars short and somewhat limited. The winner of the battles would have an incentive to conclude a quick peace in order to cement their gains before other powers found a reason to enter the war. The government of the losing state could expect the winner to offer a peace treaty that they could agree to without personal consequences like being deposed or executed. In the ACW, there were no powers that could realistically intercede on a large scale and no reason other than human feeling for the U.S. to grant the Confederates a degree of leniency.
I've addressed the lack of technological differences between the ACW and Europe in another answer
Sources:
Nosworthy, Brent "The Bloody Crucible of Courage: Fighting Methods and Combat Experience of the Civil War"
McPherson, James "Battle Cry of Freedom: The Civil War Era"
Barry, Quintin, "The Road to Koniggratz"
Barry, Quintin "The Franco-Prussian War 1870-71"