I don't think ancap would have a more equal distribution of resources if that's what you're saying.

If you can't have private production of goods and services outside of worker syndicates or whatever the particular variety of anarchist economic organization the person is proposing, then you will have income equalization at the expense of introducing major incentive problems in producing those goods and services.

The whole "owning the product of your labour" line doesn't actually ever materialize under their system because when they enter worker communes, they see the productivity of everyone abstracting into a large blob and everyone gets an equal part out of whatever this blob produces regardless of everyone's individual inputs.

So, I think their distribution of income or resources would be more equal; I just think they would end up destitute. They're welcome to try though, there certainly are companies without hierarchy that do quite well (Valve Software) - the only catch being that they hire exclusively at the absolute high end of the productivity scale and those people who are self-motivated. Most anarchists themselves don't actually have these characteristics which demand high wages in a capitalist economy, which is part of why they externalize all their personal financial problems on the people who run firms. In that sense is extremely emotional and if you say you support private property, its like a personal attack against them and they get apoplectic, as I'm sure you've seen. I suppose people could levy the same criticisms to ancaps - 'you're externalizing all your problems on the state', but its different in the sense that ancaps can define the scope to which these problems are generated. Your income tax form is very specific on how much is being taken from you; the degree to which "the full product of your labour" is not being paid to you is in some sense incalculable.

What an ancap society would do is open more opportunities to become rich and have a more competitive market for buying labour, increasing wages.