Respectfully must disagree about the Franco-Prussian war being considered the "Greatest War" because in large part it was limited in geography and time. Casualties alone should not define what is pivotal to historic consciousness, nor politics. In terms of human, literary, political, and psychological effect, as well as duration, one European conflict was incredibly memorable for all Europeans and most Americans.
The Napoleonic Wars (or more precisely, the post-Revolution wars) left an unforgettable mark on almost all continental Europe, Latin America, and the United States. In sheer duration, the series of conflicts lasted for an entire generation. While it is true that the conflict was intermittent and officially only a series of wars, the singular character of its focus, France and Napoleon, gave it a historic grounding that drastically effected the lives of famous artists ranging from Goya, Beethoven, Haydn, Hegel, and Tolstoy, all of whose artwork and literature was drastically effected by the conflict.
Major political results occurred despite the hard fought efforts of conservative Europe to bottle back up liberalism and French nationalism. Latin America gained near total independence in the aftermath of Spain's occupation and economic destruction by the French. French Haiti erupted in racial and class warfare as a result of the revolution, and Napoleon's failure to reconquer the island directly led to his decision to handle the Louisiana Purchase with America. The US itself fought a major war with England, and America, Spain, and Russia all saw their capitals burned to the ground. Germany changed too. The literary birth of German nationalism amongst the bourgeois might be traced to the conflict and the writings of Fichte and his kind, while politically the conflict saw Prussia recover from its lethargy after the Seven Years War and end up at Waterloo as a premier German military power with the cadre structure needed to eventually defeat Austria.
The world was astounded by this war. I feel it important to note that it was also referred to by contemporaries such as Pitt and Jefferson as a Great War, that it was perceived by Russians and likely a dozen other agrarian societies ranging from Spain to Egypt as the war against the Antichrist or Devil. Contemporaries viewed it as one vast conflict begun when France overthrew its legitimate government perhaps (this could messily be considered the Tory view), or when France fell into the hands of a tyrant (the Whig view).
The human cost from 1792-1814 lay in the millions. The guillotine, Empire, and Napoleon himself were defining parts of Europe's history and if neither resulted in a major rewriting of Europe's political geography, that is because the revolution led to equal and powerful counteractions. Metternich's Vienna Conference held Europe together under monarchist regimes for close to 100 years until the Franco-Prussian War and World War I smashed it apart.
A little late to the party but - while the Napoleonic Wars involved pretty much all of Europe as well as parts of Asia and the Americas, and influenced much more of the world, it's influence wasn't really felt in China and other parts of East Asia. There people would probably refer to the Taiping Rebellion as the "Great War" before the massive wars of the 20th centuries.
The Taiping Rebellion was essentially a Chinese civil war fought between 1850 and 1864. At the time China was governed by the Qing Dynasty, headed by ethnic Manchus who had conquered China in the mid 17th Century. By the mid-19th century, the Qing government was widely considered by many Han Chinese, the ethnic Chinese majority, as corrupt an ineffective. In 1842 China had been defeated by Britain in the First Opium War, and many blamed the government for this humiliation.
In 1843, Hong Xiuquan, a man from a poor mountain village with failed aspirations to be a government official, created the "God Worshiping Society," a movement which combined Christianity with Confucianism, Daoism, and other traditional modes of Chinese thought. Hong and his followers claimed they were reviving a purely Chinese form of worship, present long before the Manchu invasion and distorted and displaced by the Confucianism of past dynastic regimes.
The God Worshiping society, situated in Southern China, gained power by suppressing local groups of bandits and pirates. Open fighting between it and the Qing dynasty began in earnest with a series of battles in early 1851, when Hong's armies decisively beat back Qing forces sent to put them down. Hong declared the Taiping Heavenly Kingdom in the lands that his forces controlled, crowning himself emperor. Fighting spread into the densely populated provinces of Jiangsu and Zhejiang - the cosmopolitan and commercial centers of China at the time. The Taiping rebels managed to capture Nanjing - the historic capital of China, and even came close to capturing Beijing in the north. Eventually they were weakened by infighting and pushed back by Qing forces. Significantly contributing to their defeat was the "Ever Victorious Army," a corp of mercenaries led by the Famous British Officer Charles Gordon. Hong himself died of food poisoning after eating dirty vegetables, when food available to the rebels began to run low.
So what makes the Taiping Rebellion such a Great War?
Total War The war was characterized by massive mobilizations of the Chinese population. In the Taiping Heavenly Kingdom, nearly everyone received military training, and most everyone was eventually drafted to fight the Qing armies, especially as things started to take a turn for the worse. The War was additionally characterized by strategies which targeted entire populations - such as the burning of crops and other resources - leading to widespread famine and disease. In addition to this, both sides often massacred the populace of cities and towns that they captured. The Qing forces as a rule executed any captured rebels. Eventually they took to executing anyone they came across who spoke in the Guangxi dialect of Chinese, seeing as the rebellion began in the region of Guangxi.
Death Toll The exact death toll of the Taiping rebellion is hard to calculate - but even the most conservative estimates put the dead at around 20 million. Some of the larger estimates run up to 100 million. Going with the lowest estimate of 20 million, the conflict is still one of the deadliest wars in human history. Although it's arguable whether more soldiers were employed in the Taiping Rebellion than in the Napoleonic Wars, the death toll of the Taiping Rebellion vastly overshadows that of its European counterpart. China would not see such destruction again until the marauding advance of the Imperial Japanese Army with World War 2.
Continuing Influence The Taiping Rebellion further sapped a China which had already been vastly weakened, even since its most recent Imperial height in the mid 18th century. The war opened it up for exploitation by a myriad of Western Imperial powers, who carved out zones of influence and declared treaty ports, while an impotent Chinese state angrily stood by. Ultimately, China's weakness would be exploited again and again by Japan, in a series of wars which would culminate in the Second-Sino Japanese War - and the coming of World War 2 in the Pacific. If there was a strong Chinese state in the region, it's perhaps possible that Japan would have remained contained - as the Chinese presence had contained Japanese ambitions in the past.
Source - God's Chinese Son: The Taiping Heavenly Kingdom of Hong Xiuquan By Jonathan D. Spence