I just cleaned my Firefox addons and wondered:
Which features does Firebug have that make it unique?
Which features are available in both Firebug and the Firefox Developer Tools?
Firefox's native developer tools have come a long way since this question was written. The differences have mainly reduced to the following points:
There are more things missing, which are tracked in a bug report filed for all the gaps between Firebug and the Firefox DevTools.
Firebug integration
Firebug is now built on top of the native developer tools. Since Firefox 48 there's also a Firebug theme that looks like the Firebug extension, letting you feel at home if you're used to Firebug. Once multi-process Firefox is enabled, pressing F12 or clicking the Firebug button opens the Firefox DevTools and with the Firebug theme.
There's also a migration guide explaining the differences between Firebug and the Firefox DevTools.