Yes there is but there is no way for you to be exhaustive. The best bet is to check the last few versions of each browser with an emphasis on what your visitors use. Even one version of a browser can render slightly differently on different platforms. I have seen Firefox and Safari recently behave differently on Windows and Mac and Chrome differently between Linux and Windows.
Chrome is constantly changing and, while not every version makes it on user's machines, there are literally hundreds of versions out there. The only way to know the differences would be to look at the Change Lists but this is a monumental task.
Chrome has just changed its rendering engine to Blink which is a fork of WebKit. It will take time before most people transition to it but from this point on you have to expect that differences in rendering between browsers will increase as Safari and Chrome will no longer share a rendering engine. Opera will shift from WebKit to Blink later but that will only change the mix and not add variety.
Plenty of Linux distributions build their own Chromium which have a different release schedule which makes for plenty more potential versions. The good news is that actual differences are usually small, so it is better to check various major versions than several continuous minor ones.