Firefox Focus makes a great "default browser" for opening random links from apps, as it's always in incognito mode, very lightweight, and supports content blocking. Only real downside for me is that you are still contributing to webkit dominance, as it's chromium-based. Full fat Firefox on android is great too, though.

As a fully featured browser which supports extensions and has a good UI, Samsung's browser is astonishingly good and I believe open for anyone to use now, though again chromium-derived. I fear at this point the battle may be lost for alternate rendering engines on mobile, though.