@gergely I don't know if there's a table-like compassion of features (at most something like this: http://www.flycheck.org/en/latest/languages.html), but from experience I'd say the only reason to use FlyMake is because it's built-in, but even in Emacs 26, it's just not as good as FlyCheck.
but that's just my opinion.
@gergely it depends on your use case and (at this point in time) emacs version. I'm pretty sure Flymake got a major overhaul in Emacs 26 and is supposed to be better now, but I'm not sure how true that is (I don't use it). Anyway:
will work for most compiled mainstream languages
Cons: doesn't have support for many languages
Pros: works with many languages
easier to support new ones
Cons: not built in, so requires install.
Hope that helped a little and YMMV
@gergely ah, actually flycheck does provide exactly what you're looking for. Here you go: http://www.flycheck.org/en/latest/user/flycheck-versus-flymake.html