I develop a Firefox and Chrome extension, and I'm adding a button. It seems like a page action (button in the address bar) is the "correct" choice, as opposed to a browser action (button on the toolbar).
I don't have enough karma to post images, but you can see examples here.
However, I've done some (limited) informal user surveying, and it seems that literally nobody realizes that the page action icon is a button -- they think that it's just informational.
(This is exacerbated by the fact that a) the mouse doesn't change to clicky hand or the like on hover, and b) in Chrome there doesn't seem to be a way to change the icon on hover to indicate interact-ability. This is parenthetical because most users won't even know to try to hover.)
This is less a problem on Firefox because it's possible to put a button in both places. But in Chrome it's strictly either/or.
Are page actions obvious to the user that they are clickable? Does anyone have experience or know of user studies regarding them?