I don't know why it is, but I've noticed the exact same behavior with my local setup. I think it has to do with how it's taking to poll the database/how its connecting? One way it bounces through your computer and back only (localhost), the other it hits your local network (something to do with TCP?) and then bounces back (the IP). I've also heard that doing it via IP works faster.
But I think it actually comes down to how MySQL treats incoming connections (and it even does so differently based on what OS it was installed on). If you installed a site one way, and access it the other way, thinking it would read the same internally, you'd be surprised. The session data will think localhost is a completely different access point than 127.0.0.1, so the session won't carry over. In fact, if, when you log in via localhost, does the address bar change to 127.0.0.1 and then act like you never logged in? Mine does. And I think this is because I had to install Mysidia under 127.0.0.1 because it wouldn't accept localhost? I've had a few other frameworks I've installed which present the same mystery issue.
I think
this might be some relevant further reading.