The right-hand sentences have roughly the same kind of meaning, but generally speaking they seem less idiomatic and less likely to be used. "I am so young that I can't die", especially, feels odd (or doesn't mean what one usually would intend). On the other hand, "I'm so tired (that) I can't keep my eyes open" is natural, so the issues here are quite subtle.
New words, one handy idiom, and a 2-minute quiz — delivered to your inbox to keep your streak alive.