The developer tools are constantly being improved and often the pre-release versions of browsers can offer you something extra.
Chrome Canary is the experimental version of Chrome. Canary can be run side by side with Chrome so you can check for issues in the current release at the same time.
You can further enhance your Chrome Developer Tools by visiting the URL chrome://flags and enabling the option marked "Enable Developer Tools experiments". Don't forget to hit the "Relaunch Now" button at the bottom of the page to apply your changes.
Firefox Aurora offers a preview of the latest features of Firefox. Unfortunately, Aurora cannot be open at the same time of Firefox.
Webkit Nightly is a nightly release of Safari. As it's a nightly release, it is less stable than the other browsers. But with Safari's Developer Tools in their current mess in the production release, the nightly release fixes a large proportion of these problems giving you a usable experience. Webkit Nightly can be run side by side with Safari to check for rendering issues.
Now browser release cycles are as frequent as 12 weeks and browsers auto-update, changes are incremental and less likely to be breaking; and it won't be long (>12 weeks) before your users are using these versions. It's important to test on both the current and developer versions where possible.