In Beneath the Metadata: Some Philosophical Problems with Folksonomy Elaine Petersen argues that as folksonomy is underpinned by relativism, it will always be flawed as an information retrieval method. So, folksonomy will collapse because everything ends up tagged with every conceivable tag so they all cancel each other out and you might as well have not bothered tagging anything.
On the other hand, David Weinberger in Why tagging matters? claims that taxonomy will fail because taxonomists want to invent one single taxonomy to classify everything in the entire world and in a totalitarian style insist that the one true taxonomy is the only way to organise knowledge.
I have no idea who these mysterious megalomaniac taxonomists are. Most of the taxonomists I am aware of only advocate using one single taxonomy for fairly well defined and limited situations (e.g. a single company, or perhaps a department in a big corporation) and are quite happy with the notion that you need lots of different taxonomies suited to context, which makes them much more like Petersen’s relativists.
Conversely, I am fairly sure you can’t actually create an infinite folksonomy with infinite tags for all possible viewpoints of all possible documents (let alone smaller knowledge units). When your taggers are a specific community with a shared purpose, they probably will hit upon a shared vocabulary that is “universal” within the boundaries of that community and so the folksonomy will be meaningful.
I think that these reductio ad absurdum arguments are interesting because they highlight how both folksonomies and taxonomies are inherently flexible and even somewhat unstable, especially when they become large and very widely used. Intervention and management of both will help improve and maintain their usefulness. No matter whether you choose one or the other or a combination of the two, you still need knowledge workers to keep them in good working order!