When debugging in Chrome/IE it's always painful to use the developer tools even though they are very capable.
Inspector, HTML editing, Net panel: Basically the same.
Storage: you can inspect localstorage and IndexedDB with dev tools. You need https://addons.mozilla.org/en-US/firefox/addon/firestorage-p... for inspecting localstorage with Firebug. No IndexedDB support, but I never used it (localstorage is so much simpler) so I didn't search much. Firebug can delete cookies (maybe that's another extension, can't remember), dev tools can. It could be even, depending on what you use most.
Console: dev tools autocompletes functions. Inspection of variables is abot the same but Firebug displays more information without having to browse all the values tree. Firebug's console is multiline which is handy for typing in short scripts. However that means that commands run only with CTRL-Enter. I prefer Firebug.
HTML structure: the same but the dev tools bury the DOM tab into a right click menu. I prefer Firebug's UI.
CSS editing: the same.
Script/Debugger: almost the same but I prefer Firebug because of the way it displays information about the variables (similar to my reasoning about Console).
Aesthetics: Chrome and Firefox dev tools looks more primitive than Firebug to me but this is very subjective and I have a theory about it. Web and mobile have been moving to a minimalistic and flat design for the last few years. Having used computers since the 80s that reminds me of some designs of the 80s/early 90s. The flat Windows 8 desktop mode decorations are somewhat similar to the early Windows (check http://www.webdesignerdepot.com/2009/03/operating-system-int...) with obviously everything that more pixels, colors and animations allow. Still I can't feel it a bit deja-vu like some elements of fashion that came back after forty years (example: the brown color - Europe here, USA could be different). Younger folks will say that are Firebug's 3D buttons to look dated and I understand it. But just wait some 20 years and I bet you'll start having that feeling too :-) As I said: very subjective.
Summary: that basic functionality is more or less the same and the difference is probably more a matter of UI and habits than of technical merit. There might be some use cases where you need to dig into dev tools' options and enable more functionality. Dev tools win there.
Like with most similar consoles the Firefox dev tools allow you to create newlines with Shift+Enter