Great little app (I'm on 10.8.2). You can switch your default browser either using the menu bar icon (which conveniently displays the icon of your current browser), or by setting a global hotkey via the app's preferences.
When you press that hotkey, an overlay window pops up, displaying icons of all your browsers - to make the overlay window disappear, you need to either select one of the browsers or click outside the window.
There's also a thoughtful option to hide browsers identified incorrectly by the app (click the menu bar icon to display the browsers, then press ALT. Minus signs will appear beside the browsers; click the one you want to hide).
Suggestion: it would be nice if the same global hotkey used to display the overlay window, could also be used to make that window disappear.