On Android Chrome is arguably better if you want Google account integration or raw speed, but Firefox for Android has a more traditional UI, extensions, and is fast enough for most of my browsing.
Sorry, but unless you have a Gecko-based version (which - AFAIK - is not what you can get from Google Play or F-Droid), it's system WebView (i.e. Chromium) under the hood.
I like Firefox Nightly on Android though, it's really good.
Um
Define "googly"
(If you're saying it's atypical of the behavior you'd expect of them: based on what?) Considering there's no trivial way to log into one of their services (gmail) without automatically doing so on others (yt etc) without fucking around with browser sessions - among many other non-customizability gotchas from them - saying google doesn't want to control how their offerings are used is going to be a very tough sell.
I feel like I'm being ActiveX'd into using Chrome now which is very non-Googly. Not sure how feasible it is to use a different mobile browser until Mozilla and Google work together to make sure they're all on the same API page on Android. Ironically enough, Windows is far more open and friendly to competing browsers than Android.