I always recommend Firefox ESR to corporate clients that use our web-based product. Long-term stability, automatic security updates, and a yearly, well-documented release cycle that allows their IT department to test the upcoming ESR release and upgrade with confidence, while we get the benefit of a modern web browser to target.
ESR user for many years, plus useragent-switcher for sites that pretend to care about my "security" (but mostly care about CSS eye candy and the latest whizzbang). Free beta tester for other people isn't in my job description ;-)
Specifically this example I don't know, but there are pretty big differences between look and feel on websites when sending a Chrome UA vs a Firefox UA. The most obvious example is Google.