It's hard to pinpoint one thing. They're just much more usable and don't make you fight against it. It just gets out of your way. That's great UX design right there. Just measure the amount of key strokes, clicks, time and overall actions needed to do one thing in Chrome and the same in Firefox. You'll be amazed.
I would hope or presume that Firefox's tools eventually do get this level of polish, though. Chrome (and even Safari) has had quite a bit of a head-start, and neither of those were shining examples of great UX at the beginning.
The Opera Developer Tools (Opera Dragonfly): The UX is done well, the markup editor works even better than in chrome and I like the screenshot utility and color picker. The css inspection is inconvenient when you want to change properties or add new rules. The network log is done well but the UX can become confusing, the make request feature is exceptional I don't know any other devtool that has that integrated. No xpath in the dom inspector.
Firebug: This was the first browser devtool afaik so it has a long history and years of development behind it, I always considered it to be "the firefox developer tools" and I was really surprised when mozilla announced they would recreate it on their own instead of just integrating firebug. But I guess they have their reasons.
Firebug has a great UX, everything is fast and polished although it has become a little old, it still integrates nicely in the current firefox UI. The dom and css inspector is great, it allows to quickly change anything you ever want, with the exception maybe that you cannot add new css rules (only element styles). The network inspector is exceptional, best of all 4. I don't like the console/REPL but its alright. Overall still my second favorite.
Firefox Developer Tools: I must admit, I don't even know where to begin. The UX is just awful: From the alien dark-blue that doesn't integrate at all with the rest of firefox and the font sizes that you can't change to the strange dropdown menu/button combinations in the latest version. The DOM inspector doesn't allow you to edit html directly, has no xpath and the css inspector is confusing and doesn't has autocompletion. There is no resources overview, no networking debugging and profiling.
I do however acknowledge there is some progress in the latest snapshots, I like the scratchpad, style editor and the UI overhaul made it a bit more usable. There are still no settings, still no way to change the dark theme. I don't say it isn't making some progress, but its so slow (they say they need a few months for the python api alone), that chrome will have progressed well beyond and I don't see them catching up.