Switching between channels isn't supported anymore according to https://support.mozilla.com/en-US/questions/837315#answer-203401
The right way now is simply to download the channel you want from http://www.mozilla.com/en-US/firefox/channel/ (or from https://nightly.mozilla.org/ for nighties).
Nightly and aurora builds install into their own folder, and coexist well with a beta or release build.
Beta and release builds default to the same location, so you'll need to choose a custom install for beta versions and change the install location if you want both available at the same time - otherwise you can switch between the two by installing one over the top of the other.
See How can I install both Firefox 3.6 and Firefox 4 beta? if you need to run both versions at the same time, otherwise, if you already have a Firefox window open, from any channel, trying to run a new firefox process of any version acts as a remote for the existing one instead - ie, it will open a new window attached to the existing Firefox.
As always, back up your profile often if you run prerelease versions, and consider using a dedicated profile for testing. See https://support.mozilla.com/en-US/kb/Profiles for more information about Firefox profiles, including how to perform backups, manage profiles, etc.