Google Docs is more responsive and faster in Chrome (it improves in Firefox if you fake the Chrome UA, hah). YouTube relied on Flash much longer in Firefox, while Mozilla was working to make their MSE implementation compatible with Chrome.
Google broke YouTube for Firefox users right before the last Christmas holidays. Mozilla pushed out Firefox updates over the holidays that faked the UA as a workaround.
Google Inbox didn't work on Firefox initially, because Google claimed Firefox was too slow. When reported to Mozilla, it was fixed in a few hours, and they found that Chrome's implementation of the "thing that was too slow" was actually broken and not spec compliant.
Hangouts (used to?) require a plugin in Firefox, and just uses WebRTC in Chrome.
For more backstory, here's the Firefox bug report with the fix for Google Inbox being "too slow" due to JS array slice being faster in Chrome than Firefox due to a V8 bug:
When you change the user agent in Docs, the JS app tries to use a webkit-specific selection API and just crashes. The timing results for that test seem bogus.
Google broke YouTube for Firefox users right before the last Christmas holidays. Mozilla pushed out Firefox updates over the holidays that faked the UA as a workaround.
Google Inbox didn't work on Firefox initially, because Google claimed Firefox was too slow. When reported to Mozilla, it was fixed in a few hours, and they found that Chrome's implementation of the "thing that was too slow" was actually broken and not spec compliant.
Hangouts (used to?) require a plugin in Firefox, and just uses WebRTC in Chrome.
And so on...(sigh)