In chrome://flags there is an option "LCD text antialiasing". On my system (OS X 10.11.6, Chrome 62) I've taken zoomed screenshots and don't see the blocky colors that are "bad" anti aliasing with it left at default and it's usable. But I've adjusted the OS font rendering settings from default.
I remember that Chrome removed GDI leaving DirectWrite font rendering on Windows, would be interesting to see if this helps anyone.
It's usually pretty easy to see the font antialiasing in action. Take a PNG (uncompressed) screenshot and zoom it in. Firefox Quantum seems to be an odd case though 😐