Just adding some talking points as someone who uses Firebug / Chrome Inspector every day:
At the time of writing, there's only Google DOM inspector and no it doesn't have all the features of Firebug
Inspector is a 'lite' version of Firebug: The interface is not as good IMO, element inspection in both recent versions is now clunky, but Firebug is still better; I find myself trying to find the love for Chrome (since it's a better, faster browser experience), but for development work, it still just sucks for me.
Live preview / modification of DOM / CSS is still way better in Firebug; calculated CSS and box model view are better in Firebug;
Somehow it's just easier to read/use Firebug maybe because of the ease of navigating, manipulating/modifying the document in several key areas? Who knows. I'm used to the interface and I think Chrome Inspector is not as good although this is a subjective thing I admit.
The Cookies/Net tab are extremely useful to me in Firebug. Maybe Chrome Inspector has this now? Last time I checked it did not, because Chrome updates itself in the background without your intervention (gets your consent by default like all good overlords).
Last point: The day that Google Chrome gets a fully-featured Firebug is the day Firefox basically dies for developers because Firefox had 3 years to make Firefox's layout engine Gecko as fast as WebKit and they didn't. Sorry to put it so bluntly but it's the truth.
You see, now everyone wants to move away from Flash in lieu of jQuery motivated by mobile accessibility and interactivity (iPhone, iPad, Android) and JavaScript is 'suddenly' a big deal (that's sarcasm), so that ship has sailed, Firefox. And that makes me sad, as a Mozilla fanperson. Chrome is simply a better browser until Firefox upgrades their JavaScript engine.