In GNU screen, I could type Ctrl+A twice to switch between two windows.
In byobu, I can't see how to do that. F12+Ctrl+A doesn't work, and I can't find anything in the manual.
To be clear, I do not want to change the escape sequence to Ctrl+A. I want a key sequence that would switch between current and previous window.
I just moved my .screenrc out of the way and tried this.
On my machine (Oneiric) both F12-Ctrl-a and Ctrl-a-Ctrl-a worked exactly as I would expect.
I think you have another problem? Maybe something else is swallowing your key presses?
On my system, F12+Ctrl+a works fine.
Despite that, you can use F3 and F4 to move to previous/next window. You can access the shortcut list using F9 -> Help.
Toggle the menu by pressing F9.
Under Change keybinding set choose screen-escape-keys.