archaic might have been a bad choice of words, although it probably depends on the exact sentence. I do think it sounds more formal, though, I think I'd be less likely to hear your first sentence in everyday conversation. Then again, I'm not a native speaker of English.

My native-speaker intuition tells me the opposite — I’m probably more likely to use such constructions in colloquial speech than in formal written text. My second sentence does seem more formal to me though.