As a Marxist-Leninist, the biggest distinction is that Marxists and Anarchists have different views of what the State even is, to begin with. As a consequence, what a society that has abolished the state looks entirely different for Marxists and Anarchists. We can’t all get behind the ideas you posited, specifically decentralization as the basis for the economy.

For Marxists, the state is an instrument of class oppression, and to eliminate it, you must eliminate class. An important note, class is not hierarchy. There exists inter-class hierarchy, such as bourgeois and proletarian, but also intra-class hierarchy, such as managers and workers. A fully publicly owned and planned global economy is what Marxists envision as “Communism.” Without any property distinctions, there is no class, and thus no need for special bodies of armed men to uphold property distinctions, no need for things like property rights, while things like administration remain.

This is because Marx’s view of Socialism is as it emerges from Capitalism. As Capitalism advances, large industry emerges, and with it cooperative production and increasing complexity in fewer and fewer firms. Marx therefore saw the Proletariat, growing greater in number and the bourgeoisie lesser and lesser as competition dies out, as taking control and directing this new economy in its own interests. It isn’t about reversing trends into decentralized communes, as in Marx’s eyes, this retains class distinctions, as each commune only owns itself, and thus there is no mechanism for equal ownership across communes, and therefore a necessity for a “state” in each commune to protect these rights and competition between communes for production and trade.

For Anarchists, the state is about hierarchy. Tackling this is the primary objective. This is why when Anarchists judge Marxists on their ability to abolish what Anarchists percieve as the state, they find Marxists invariably fall flat. However, when Marxists are judged on their own merits and own goals, we find Marxists to be quite successful.

As a side-note, the vanguard structure is a formalization of what already exists, the politically advanced among the revolutionary class. It isn’t distinct from the revolutionary class. I recommend reading The Tyranny of Structurelessness.

I over-simplified a ton, but I hope this helps! I can also answer any questions you may have. I used to be an Anarchist myself, so that helps smooth miscommunication.

I also elaborate on this subject here.