Though with water cooling you might also have a lot of pump noise, especially if the radiator is mounted incorrectly.
The larger the diameter of a fan, the lower the RPM it can spin at to move the same amount of air (same cooling capacity) as a small fan. Provided you can put the air where it's needed (e.g. a 1 foot fan can't "focus" air onto a 6 inch radiator) a larger fan will just about always be quieter and more efficient.
Oh, and having a water cooled PC with the radiator and fan inside the PC itself is silly. If you run the pipes outside or into your basement, your PC is almost completely silent, plus the cooling capacity will usually be much, much higher, because not having to cram fans and a radiator into a small enclosure lets you make them bigger and more efficient.
And historically, bigger case fans have been problematic, those 200mm fans they tried to introduce some years ago. Bad static pressure if I recall correctly?
Also, I wouldn't call having a radiator and fan inside the PC silly. The case eats a lot of the noise already, it's the easy and the common setup, and good AIOs are quiet and cool well. But maybe you just wanted to share a cool big water cooling setup with everything noisy routed into the basement ;)
In my case I have a DDC style pump, and its very quiet after I got a car wash sponge and cut a square hole in it and put the pump inside. It looks ghetto but its inside a case so who cares.
At first I was worried about heat, but its lasted 10 years so far.
I heard a story about a DIY PC that did nothing but circulate water through the cpu cooler from a fish tank; the tank was big enough to dissipate heat through evaporation and other means, only occasionally needing a top off.
I actually mounted an automotive transmission cooler to the outside of my PC and made it part of the watercooling loop, because it was inexpensive and large. There are no fans on it, but it still reduces the work the standard pc cooling radiator with the fans on it needs to do.
