In Firebug, there was just one window and it would become the debug window for whatever page you were on, in the browser. (although you might have to 'enable firebug for this page')
With the built in Dev tools, it seems you need a new window, for each page you want to work on. Can this be changed?
The Firefox DevTools do not have this feature yet, unfortunately. Though it is requested in bug 1219917.