What was the conflict between Marx and Bakunin, philosophically speaking?

From Reddit:

Most basically, it came down to the role of the state in revolution. Marx had theorized that society would progress from capitalism, the political and economic dictatorship of the bourgeoisie (capitalist owning class), to socialism, the political and economic dictatorship of the proletariat (working class), to communism, which would be classless and stateless. Marx's vision of this transitional socialism entailed a revolutionary state, controlled by the working class. I'd note here that Marx did not use the term "dictatorship" as we now do, to mean autocratic rule, but instead theorized that every society is controlled by a certain class, which is the one that controls productive property, and that the state effectively serves the interest of this class. This is why he theorized that there must be a dictatorship of the entire working class to achieve communism (which would be stateless).

Bakunin, the most influential anarchist of his time, saw the state as a fundamentally authoritarian institution. He held that the abolition of the state was necessary for the true abolition of capitalism and the exploitation and alienation that went with it. On this topic, he wrote, “How can a free and equal society arise from an authoritarian organization? It is impossible.” To Bakunin, the state was not a tool that could be used to reach a stateless society, and any such attempt would lead to a dependence upon that state. While Marxists contended that anarchists could never succeed in the long term, anarchists held that Marxist revolution would not lead to a truly free society.

This difference was really brought to the fore in the aftermath of the Paris Commune of 1871, a two month long revolution in which the workers of Paris seized control of their city, raised the red flag, and instituted the most radical program ever devised at that point in history. See this post for more specifics. Both hailed it as the first great working class revolution, but because of the way the Commune was run, anarchists claimed that it was stateless and Marxists claimed that it represented a revolutionary state in transition to communism. Marx also held that the Commune ought to have centralized power, which put him at odds with Bakunin and the anarchists. Ultimately, this is what pushed the two over the edge, leading to the expulsion of Bakunin and the anarchists from the International Workingmen's Association.

In addition to the role of the state, a major difference was that while Marx was a communist, Bakunin was a collectivist. Anarchist communism would later become the dominant strain of anarchism after Kropotkin's works at the end of the 19th century, but at this point, collectivism dominated organized anarchism. While communism holds "from each according to his ability, to each according to his need", collectivism does not abolish currency and allows for some variation in wealth. However, at this point historically, this difference was not so important as the difference in revolutionary methods. Both were ultimately advocating collective ownership and direction of productive property by the workers, and the ultimate goal of a classless and stateless society.