There has been quite a lot of discussion about this issue lately, not least in the thriving 'ancap Vs ancom debate' group on facebook but it comes up everywhere, I'm hoping to add to the conversation with my thoughts,
Note; I'm not attempting to defend "anarcho-capitalism" (I'm a mutualist with communist sympathies).
A Short History
Anarcho-communism got thought up in societies where peasant-village collectivism was the dominant way of life as industrialisation, the cumulation of the centralisation of state power and anarchist ideas were spreading in the later half of the 19th century.
At the same time market/ individualist anarchism arose in societies where small scale industry and trade was very much a thing as industrialisation and the centralisation of markets in an alliance of capitalists and the state came about.
To the adherents of both it seemed obvious what would happen if you removed the state from the equation: In places like Russia (where Bakunin and Kropotkin were thinking their great thoughts) the peasants would have been left alone to live in commune like villages. In places like the USA (where people like Spooner and Tucker were thinking their great thoughts) if you removed the state people would have been left alone to trade freely.
When individualist/ market anarchists met anarcho-communists/ collectivists they didn't understand each other. An coms wondered why individualists were so obsessed with markets and competition, it sounded too much like people could still end up exploited by big business in their proposed society. Individualists didn't get why comunes were so important to the communists. It sounded too much like communism would be forced onto people.
Some individualists explained that people would be free to live in communes if they wanted to, in a market anarchist society and some anarcho-communists explained that joining a commune would be optional in an anarcho-communist society, there was, and still is lots of confusion and misunderstanding within the two groups. Today more than ever it is common for both sides to
wonder if the other are real anarchists at all.
Their critiques of modern society
In my opinion individualist anarchism has a much more striking and relevant critique of western capitalism/ statism and therefore of the whole global economy which it now dominates. Example: I was reading an article shared by an ancom about boycotting some big American football event in the USA, the reasons given mainly centred around the fact that it is a brutal game and that some prominent players have been accused and some found guilty of rape and violence against women and got off very lightly by their bosses at the clubs. I agreed with the violence against women bit, if there is a culture of accepting that then that's disgraceful. I didn't care at all if it was a brutal game, I'm not the players mummy, they can choose to play a brutal game if they want!
What wasn't mentioned was that big sports statiums are usually built on land seized by the state, that the police provide them security for games paid for by money forcibly extracted from people by taxation whether they like football or not, like how they receive all kinds of other subsidies from the state (and tax breaks), like how their kits and other equipment are made in sweatshops in countries where rigged "free trade deals" struck up between US govt and the govt of whatever poor country is making them are keeping millions in poverty.
Why wasn't this mentioned? Because anarcho-communism as a theory, in my opinion, just doesn't have much to say about that stuff, it certainly doesn't have anything very original to say.
In conclusion they are both proper anarchism but they have been promoted by flawed humans who couldn't or didn't want to understand each other because they want their thing to be the best. But in my opinion market anarchism has much more to say to the world right now than anarcho-communism does.