Ignoring the theory, the philosophy, or the various emotional and psychological factors that might lead a person into one belief or the other, what is the actual, working difference between the two systems? I think I can offer a somewhat unique perspective.
In either case, a person can make a claim to ownership of a resource. But when they do this, what's actually happening? What does it mean to own something? It means it's illegal for other people to take it away from you, and, in most circumstances, for them to use it without your permission. Seeing as how what is or is not legal is just a matter of what people are willing to enforce, so what is or is not your property, being a legal construct, is also just a matter of what people are or are not willing to enforce. When a person makes a claim to ownership of a resource, what they're doing is asking their society to consider any violence used in defense of that claim to be legitimate. The society is then able to accept or reject this request.
The difference between a society under anarcho-capitalism and one under anarcho-communism is that they would have different standards for determining which claims to ownership are considered legitimate and which are not. Left-anarchism is an attempt at creating a standard of ownership that would facilitate the creation of an economy wherein the average person has more control of their labor than they have now. The usual way that people think this could be accomplished is by deciding to only enforce claims to ownership of land or infrastructure made by the people who personally use or occupy that land or infrastructure.
The PR problem that left-anarchists have is that they spend too much time talking about the symptoms and not enough time talking about the disease, which leads people to think they want to make certain components of a modern economy illegal, thus making them seem rather authoritarian. For example, left-anarchists talk about wage labor as though a crime in itself, despite having no actual problem with wage labor aside from the fact that they think private ownership of land and infrastructure systematically pressures people who would otherwise not be interested in wage labor into accepting it en masse.
It's certainly possible that in a stateless, decentralized society, both right-wing and left-wing communities would exist, and which you go to or choose to live in would probably just depend on your preferences. I think an-caps and an-coms share the vast majority of their long-term goals.