While, as @Casey describes, they did take it out of the about box (see Update on Channel Switcher. They still have the idea of channels. There just isn't a GUI for it anymore. Instead you need to edit the file
defaults/pref/channel-prefs.js in the Firefox application directory and update the value of
app.update.channel. Do not make this change in the
about:config because this is an application-level pref (not a profile-level one).
What is a little confusing here is they pushed the release version into the beta channel. So even if you are in the beta channel you got the release version. If you look at app.update.channel you will see "beta" is defined as "Betas, release candidates, and final releases."
In theory, if your app.update.channel is still beta, when the next beta comes out you will upgrade to that. I'm not sure if that will be a beta of 5.1 or a beta of 6.
With that last point in mind, if you haven't already, I highly recommend changing your updates setting to "Ask me what I want to do" so you will have some warning. You can change it in Options/Advanced/Update. Note that this seems to be (incorrectly IMHO) a profile-level setting, so you need to do it for each profile you are using.
Also see some related discussion at Beta channel switched automatically to release.