I tried to Thinapp both Firefox and Chrome, and ran into severe problems with both.
Firefox: Flash causes the browser to hang. From browsing this forum, it seems that this is a very common problem.
Chrome: The browser is very unstable. Plugin/webpage processes crash all the time. Also, downloads do not work. The first ~100 KB gets downloaded, after which the download is stuck forever. Attempting to download anything after that results in Chrome pretending that I never clicked on the download link.
Also, both browsers were slow and generally unresponsive.