NoiseTrade isn't a co-op, and in fact is a third-party middleman (a "pimp") once again. They make their money off of tips - when a fan decides to tip an artist through the platform, NoiseTrade skims 20% plus processing fees.
The various types of co-op are fairly well-defined in general, but likely the best system here would be that the member artists would have control over the running of the site (likely through a voting system or consensus system), and therefore have control over how it's funded.
This would mean that there isn't a middleman who can skim more money than is necessary for the operation of the site, because the artists own it. Even if they decide to outsource the running of it, they can still decide to fire the outsourced company/individual and have someone else run it instead, without losing their data or their network effects.
They can't do that in a situation like NoiseTrade, where the artists are customers just as much as the fans are, and have no ownership over the system; everyone's stuck there due to network effects, until NoiseTrade do something extremely egregious.