IIRC Firefox already implements the Chrome Debugging Protocol (https://developer.chrome.com/devtools/docs/debugger-protocol), which e.g. would mean that it should be possible to use Firefox's debug tools to debug web pages in Chrome (and vice-versa). Would be nice to have some clarification on this though.

EDIT: Some more clarification, apparently this is enabled by an official add-on (called "Valence") which is shipped by default on Firefox Developer Edition: https://developer.mozilla.org/en-US/docs/Tools/Valence