I’m sticking with Firefox which is by far the fastest for me (especially on popular websites like Reddit and Facebook that are way too sluggish on Chrome).
Chrome for the occasional websites that don’t work well on Firefox (e.g. Binance, for some reason), and also when I need to use a few extensions that are better in Chrome (a dark mode for websites that inverts CSS, “Deluminate” is just about the best; and some text-to-speech thing that allows me to tweak speed on Chrome but not on Firefox).
Honestly, as much as I support the concept of BAT, I’m not really sure that it’ll be practical to hope that most people switch from Chrome and Firefox, especially when the former is standard on most smartphones (85% of the market for Android iirc?) and even Edge that’s now becoming quite good too (standard on Windows 10 obviously).
These 3, imho, will be more popular than Brave for a long time. It’s not like most people care about rewarding websites, in general, but switching browsers to do that is a tall order. What would work best for BAT is as an extension for other browsers that both blocks ads and substitutes them with BAT.
UC Browser SHAREit MX Player