Maybe I'm doing something wrong. When I click inspect element, it first opens the dev tools and then inspects the body and after a moment of loading it hops to the correct element.
That moment of loading is what I expect from both FF's and Chrome's tools, neither is instant. But the last time that I used Firebug (which was almost two years ago, mind), opening Firebug would lock up the whole browser for several seconds, and then once it was open it would manage to slow down every other tab as well (which meant that I only kept it open while necessary, which meant that I'd have to endure the lock-up again the next time that I wanted to do anything).