Well, when it's not a hidden service, it's the exit node that gets to see the contents of the message before sending it (unless it's SSL of course) to the wider Internet. If there was a unique ID within the Tor network, no one on the wider Internet would be able to see it. My thought was that if you were connecting directly to a hidden service within the Tor network, there might be a unique ID. Sounds like even connecting to hidden services within the Tor network is done indirectly.