That depends on the language support for the editor in question. Emacs can check C and related languages on the fly with flymake. Emacs can also check JavaScript on the fly with js2-mode. Editors such as BBEdit and TextMate cannot do that as far as I know. I'm not sure about the others that I mentioned.

The sky is the limit with programmable editors like Emacs and vim. Like general purpose hardware and OSs, neither can do anything that the other cannot do. Emacs does have an edge but in practice people have been able to make vim do just about anything.