In my opinion they both have atmosphere in spades - KH shoves it in your face with all its cartoony cuteness whereas you might find the Capital Wasteland a bit dry (pun sort of intended) unless you go looking for all the extras.
As for immersion (usually goes hand in hand with atmosphere), I didn't find KH particularly immersive, probably thanks (again) to the cartooniness (is that even a word?) Fallout on the other hand I found very immersive, much to the detriment of my classes at the time.