Speaking from personal experience doing user support in firefox IRC channel on freenode and formerly moznet, the vast majority of "resource hog" complaints are due to the user running AdBlock with a million block rules (or some similar addon). Occasionally it is a particular long running website with JS memory leaks though. Like a gmail pinned tab.
In terms of performance, until recently a common issue was lack of default graphics acceleration on linux, requiring manually enabling layers.acceleration.force-enabled
Firefox has a suite of `about:` URLs[1], one of them is about:performance which will show you the Task Manager (their name) which has a sort of CPU and RAM column. It even shows you when it's javascript on a tab chewing up resources and not the extension.
I don't know if the situation has improved, but at least in past it seems about:performance has a problem picking out problems created by an addon doing a ton of DOM manipulation that chews up resources in the tab. Bisecting addons or my preference, a clean profile or safe mode, was usually what I suggested, but YMMV.
I've had so many issues with the Firefox Developer edition I stopped using it and have switched to Opera for my browsing needs.
Way more reliable, doesn't constantly hang and time out, and isn't a total resource hog like Firefox has become.