I've been wondering, if my system draws about 400W at peak, which PSU would be quieter? assuming both are from the same manufacturer using the same type of fan and cooling mechanism? My theory was the 1200W PSU would be quieter, because it's only running at roughly 33% load, versus a 600W PSU running at 66% load. Has anyone ran a test of this scenario?
If this is an abstract question, I'd say that nothing changes. If the two PSUs have the same components and cooling mechanism, since the power drawn is the same, I expect the heat produced would be the same, so the fan should spin at the same speed on the two PSUs.
Also, consider that a PSU has its maximum efficiency when it is run at about 60-80% of its maximum and the efficiency diminishes with load. This means that more energy is lost in the circuitry (in form of heat). A 1200 W psu would be tuned for maximum efficiency at a higher power, so it would be less efficient than a 600 W PSU at 400 W.
In a real scenario, I'd also take into account that a 1200 W PSU might have better components than a 600 W PSU from the same manufacturer, to ensure better stability at higher power loads. This could bring better overall efficiency and reduce the heat produced, and thus the fan speed.
To have a more experimental answer to the question, you can read these two reviews of the same PSU model (550 W and 1200 W) performed by the same website. Unfortunately the fan noise is below the least audible level for both the PSUs, but you can see that the fan noise only increases when the 1200 W PSU is loaded with more than 900 W.
I'd say if you want a quiet system get a fanless psu instead so long as you have sufficient airflow through your case. Tom's Hardware reviews some here http://m.tomshardware.co.uk/power-supply-silent-passive,review-32488.html