If Twilight Zone were being broadcast now people who like things like Farscape, Firefly and Buffy would despise the moralizing, sentimentality, obtuse lack of self-awareness and general unhipness of Twilight Zone.
The more recent shows are filled with self-awareness? For sentimentality, substitute unapologetically adult drama. I like Farscape more than the others you mention, but shows these days seem embarrassed to deal with human issues straightforwardly, and think they need to add a sort of ironic wink as if to say "It's all just TV, don't worry about it". Ironic, dark humor is great, and Farscape had some of that. Buffy and too many other contemporary shows, though, went for a sort of light, teenage, often witless jokiness, that got irritating.
These shows certainly seem certain that they represent some sort of "hipness"... to me it's a sort of mass-produced, lighter substitute.