In usual Google fashion, the Hangouts app has been not receiving the love it needs to stay up to date.
I heard somewhere, that Hangouts does not use webRTC(why it needs a plugin on Firefox). In general, Hangouts is most often a terrible experience.
Hangouts on Chrome switched to WebRTC in 2014 (when Chrome was phasing out browser plugins itself), but, at least at the time, it used nonstandard Chrome extensions to WebRTC and internal APIs, so that version wasn’t portable to other browsers. Not sure whether that has changed since.