I'm a relatively new web dev and I've been quite happy with Firefox's Web Dev tools. What does Chrome's dev tools give someone that Firefox's doesn't? I can edit css on the fly, see where a css rule is being overwritten, debug javascript, etc.
I use FF for 99% of dev, open Chrome maybe once a quarter. It’s a better browser.
Basically, you can press "ctrl S" for save, straight from the dev console. In FF, you have to manually designate the save location each time. It may seem like a small thing, but it's an entirely different workflow.
For frameworks that don't use plain stylesheets, it may not be useful.