Perhaps it is unsurprising, but it remains relevant. In a set theory that allows infinite sets, but does not allow the axiom of choice, you can construct the Hilbert hotel, but not the Banach-Tarski paradox, if I understand correctly.

On the other hand, to me it sounds like the distinction may also come from the difference between countable infinities (which Hilbert's Grand Hotel is limited to), and uncountable infinities (which BT depends on).