What can I do with content types that I can't with taxonomies?
Taxonomies allow hierarchical nesting of items in vocabularies, and each term can only be in one position and one vocabulary at a time.

Nodes, however, can be tagged with any number of terms from any number of vocabularies.

Tagging taxonomy terms with other terms from other taxonomies, or with other terms from within the same taxonomy could potentially have very different results than maintaining a separation between terms (descriptors) and nodes (content that can be described), especially when it comes to using something like Views to sort and separate content based on descriptors.

So it's not so much that content types can do things that terms can't, as it is that content types cannot do as many things that nodes ought not do.