Looking at it strictly from a technical level, there is little difference between a private interconnect and the connection between an ISP and their upstream provider if they have one. (we might consider debating this assumption especially in terms of scale :-))
Actually, the traditional point2point link between any two ISPs is a private interconnect. It does not have to be a provider/subscriber relationship.
--bill
Except for what one does to/with the routes learned via the BGP session involved in such an interconnect... With a "private interconnect" between "peers" one does not redistribute routes heard from one peer to another; with a "upstream" - "downstream" relationship, one does redistribute routes hears from one peer to another, thus giving the "downstream" transit to those other peers. I'm clarifying for others; I know you understand the difference :) Avi