I feel your pain. It's the only downside of the machine. Certain games seem to make the fans work much harder yet the same games on my XB1? Silent.
They should have gone the same route as the XB1. Bigger case to house a bigger fan and maybe an external brick too. The temps are supposedly similar on both (no idea how given the size of the PS4 and taking into account the PSU is internal) but the noise certainly isn't.
I don't think they could do anything about it now unless they brought out a new model. No doubt if they do that they'll go even slimmer and it'll probably be even louder!
My only gripes with the PS4 are the noise and the awful battery life on the DS4. Other than that, I'd personally choose it over the XB1 every time.
Horizontal flatDo you both have your consoles horizontal or vertical?