Honestly, I think the Series X will be quieter than the PS5. The main reason is the overclocked speeds of the PS5 GPU. Unless Sony invests a lot in a remarkable cooling solution, I honestly doubt it will be a quieter system... And I say this as a noisy PS4 Pro user.I'm hoping the PS5 has a better (quieter) cooling system than the PS4 Pro I have. That thing sounds like a jet lifting off in some games. And it is not from dust inside, because it did this since it was new.
The PS5 most probably was aiming to those rumored 8 or 9 Teraflops, and after seeing the 12TF of Xbox Series X 52CU GPU, they decided to overclock their PS5 36CU GPU to 2.26GHz (which people say it is a lot for a GPU) in order to not stay that far behind. Those frequencies will make the console much hotter, although maybe the APU is smaller than that on the Series X and that helps in thermals.