I'm familiar with the reasons for these superstitions, but I can't find any estimate of how old they are. Is one older than the other?
The superstitions are probably quite old, because they originate in the spoken language.
The Chinese word for four, written "si" in Roman characters, is a homonym with the word for "death" and therefore unlucky.
(My father (an immigrant from China) once warned me not to read a book behind someone playing a game unless I wanted him to lose because the Chinese word for book, written "shu" is a homonym for "lose.")
I was reminded by Kenny LJ that the Chinese word for eight, written "ba," is a homonym of a word for prosperity or "development." Slightly mispronounced, it is part of the Cantonese New Year's greeting, "gong hei faat choi," which literally translates to "good wishes for developing wealth."