do you really need the fallback? i've yet to need chrome for anything, since i rarely use google products other than maps.
i've found the use of google captcha on governmental, financial, and some commercial sites frustrating though. i'll abandon a site that has google captcha if usage is anything less than critical.
Like you alluded to, some websites perform much better in Chrome (in particular Google's own websites, but there's some other offenders like roll20.net).
There's an FF extension called Buster made someone here on HN that helps workaround Google's current generation of captchas. It doesn't work 100% of the time, but the success rate is still higher than doing it myself.
Some sites need NoScript disabled to work. Even using the "temporarily trust everything" option doesn't work. Since it's easier to just paste the URL into chrome than disable a plug-in and remember to re-enable it later, I do that.
linkedin doesn't work for me on firefox, so i rarely even attempt to use it. but if someone a care about wants to link to me, i have to use chromium for that.