Galaxy Nexus isn't really outdated. I'll admit it doesn't have the latest and greatest CPU, but dual core A9 OMAP-4460 at 1.3 GHz is not bad at all. The stock browser just is more fluid for me on this phone.
I have 3 Android devices from Google and all run Chrome beautifully. Maybe you need modern hardware for it to work well? I'm new to Android so I don't know. I love Chrome though..