Last time I asked around about this question, the answer was surprisingly “probably not much”! When a low-power x86 chip (like those mobile chips) is idling (which is pretty much all the time if all you are doing is hosting a server on it) it consumes very little power, about the same level as an idling Pi. It is when the frequency ramps up that performance-per-watt gets noticeably worse on x86.
Edit: My personal test showed that my x86 laptop fared slightly worse than my Pi 3 in idling power (~2 watts higher it seems), but that laptop is oooooooold.
Usually I sympathize with sentiments like this (“people use X because of uncontrolled circumstances”), but browsers are not one of them.
If you have a website that requires the use of Chrome, then just use Chrome for that website! It’s not an either-or thing – you can install both browsers and use Firefox as the primary one.
And that’s what makes this statement so problematic. You don’t earn anything by staying exclusively on Chrome, when both it and Firefox can work alongside each other.