That's assuming a rather broad definition of "hierarchical power relationships". The only power people have over each other in an anarcho-capitalist society is that which is granted voluntarily. If people choose to form hierarchies, on what basis do the anarcho-syndicalists justify coercive interference against those relationships?
I guess I'm not familiar with examples of anarcho-syndicalists justifying coercive interference against those relationships. At most, I could hear an anarcho-syndicalist arguing that such relationships aren't really anarchistic in nature, and then an anarcho-capitalist disagreeing with that assessment, and then that's the end of it (after some fruitless arguing.) If people re-align themselves into structures that mimic what we typically think of as a governing hierarchy, is it anarchism? An anarcho-capitalist would argue that a person always has the right to sell themselves into slavery. Maybe, but is that an anarchistic relationship? Does a person have the right to allow someone to initiate violence (or a threat of violence) against them? Is it still anarchism if that's done voluntarily?
If you take the exact same roles that are provided by the government today and put them into private hands, suddenly it's OK? The underlying power structure hasn't changed one bit. What's the difference?
First, that's a big "if"; capitalism does not require or imply highly concentrated ownership of property. That does, however, tend to be a consequence of corporatism, the use of political power toward the aggrandizement of certain wealthy or well-connected individuals or organizations.
We'll have to disagree on the nature of capitalism. I'm sure you've heard all of the arguments against it, and I've heard all of the arguments for it. I maintain that it necessarily results in the concentration of wealth in the hands of a few, with or without government interference, while the anarcho-capitalist argues that it's only government interference that allows such wealth to accumulate. No one is changing anyone's mind here. I'd go one-further and argue that it's the nature of civilization itself, with our class stratification and division of labor and land ownership that necessarily results in the consolidation of wealth and power in the hands of a few, and as long as we continue to organize ourselves in this way, there's no way around it, regardless of the economic system we attempt to use. There are some upsides to civilization, but that's one of the downsides.
Second, even if wealth is concentrated, that does not mean those with more wealth have "power" over those with less.
Again, here is another major point of disagreement. Those with control of property can deny the use of that property to others. If all property is already claimed (land and resources are finite) then some people are going to be fully reliant on the property of others in order to live. You can argue that it's voluntary, but as long as the owner can decide the fate of the workers at a whim, it's not exactly a relationship entirely without coercion.
I'd argue that the closest things we've seen to anarcho-capitalism are the old "company towns" which usually were pretty disastrous for the workers when in the hands of less-than-enlightened ownership.
You are glossing over at least one very important distinction, which is how those guns are used. Any security organization worthy of the name will naturally have the ability to act coercively; that's their purpose. However, the difference between a genuine security organization and a government (if perceived as legitimate) or criminal organization (if not) is that the security organization only uses its coercive abilities defensively, to counter prior aggression. A government / criminal organization is not so selective. As you say, the latter practice aggression simply "because they can, because they have the guns."
I'd argue that the difference is largely irrelevant. Any company is going to behave in a manner that maximizes profits. If they can do that through straight-up theft, no amount of philosophizing is going to stop them.
What's the difference between existing governments, criminal protection rackets, and private security forces? One is the law, one operates outside the law, and one operates within the law. Why would a private security force act differently than a criminal protection racket if it was no longer subjected to the law?
I fully expect some organizations would make the attempt. However, even ignoring the resistance they would face from rival organizations, such acts would be clearly recognized as criminal and illegitimate.
And then what?
If there's money to be made, why would rival organizations not also participate in that? Why would people view that as illegitimate and criminal, but they don't view the way similar organizations act today as being criminal and illegitimate? What would change?
Governments get away with collecting taxes not just "because they have the guns" but also because far too many people see them as "legitimate" and refuse to stand up against them, even going so far as to demonize their neighbors who do choose to resist.
So why is this a problem to an anarcho-capitalist? People are voluntarily surrendering themselves to government authority. Do they not have the right to do so?