There's not a modern society that can handle switching their counting system from one base to another, and a person that tries is basically just trying to learn to count all over again, except they already know how to count "wrong." Base2, base12, and base60 all have a few things in common, they're all highly composite numbers and are used in wide scale applications. Base12 is "better" than base10 pretty much only based on 12 being highly composite. Though if you look at the English language "twelve" doesn't exactly say "2+10" the way thirteen says "3+10"

Another thing to consider, when counting in Base(n), "n" is always rendered as "10" If something is actually in base12 then ten would usually be rendered as "A" or "a" and eleven would be rendered as "B" or "b"

Base12 isn't going to be better to use in pretty much any modern person's life, but if a hypothetical new society emerged independent from our, base6 or base12 would almost certainly be more useful than base10.

Though using base6 can be pretty easy for most people; you can think of one hand as the "ones" place (is usually use my right hand) and the other hand as the "sixes" place. count on your fingers as normal until the "ones hand" is full, when you reach five. Then you add one by closing the "ones hand" and opening one finger on the "sixes hand". If you repeat this (and have all your fingers) you should be able to count to thirty-five on just your hands! Doing this might also help you notice that thirty-five renders as "55" when written in base6.