I think there's some overlap, but I think TOS and TNG are two different fandoms that too many people try to pass off as one, when I think it's actually not. If you like TOS and TNG, you're really part of two fandoms.
Again I think a lot of people like a lot both and that's not really surprising-if you love Picard and Data you'll probably love Spock too and like Kirk (though OTOH if you love Kirk and just like Spock you may well not like Picard).
TNG is a weird case, it had no staying power with the popular conciousness
Certainly not the wider culture across the world.
Most of the general public finds sci fi in general boring at best, and is also pretty uninterested in anything older than 15 years ago, and yet I think even they acknowledge that TNG (as well as the original) is huge and loved among sci fi fandom so it still has at least some indirect good reputation among the general public.