Automated UI tests are clearly great at checking for functional regressions but they are also useful for performance testing. You have programmatic access to the same information provided by the network inspector in the browser developer tools.
You can integrate the YSlow (http://yslow.org/) performance analyzer with PhantomJS, enabling your CI system to check for common web performance mistakes on every commit. YSlow came out of Yahoo!, and it provides rules used to identify bad practices, which can slow down web applications for users. It's a similar idea to Google's PageSpeed Insights service (which you can automate via its API).
However, YSlow is pretty old, and things have moved on in web development recently, ...
