Across similar models from the same manufacturer, differing only in BTU, which are quietest when operating at the lowest setting to cool the same room?
In order words, are larger (and more expensive) units quieter (as is the case with computer fans for example), so it's worth paying a bit extra for an over-sized A/C unit, in order to get lower noise levels?
I'm interested particularly in window A/C units.
Home Depot lists decibel ratings, and in this comparison of four Frigidaire models, the largest one (also the most expensive, which suggests they might've included additional soundproofing, or used higher quality components) is half as loud as the others. BTU capacity doesn't seem to correlate with the dB ratings.
When it comes to Haier window units, which specifically optimize for quietness, the 6050 BTU model is rated at 43 dBA, while the 8000 BTU one is rated at 46 dBA.
It's tough to get good data on this, because noise levels are not always specified on AC product sheets, especially when there are multiple fan / cooling settings. A couple of quick google searches show contradictory findings: noise increases with cooling capacity, and noise is not correlated with cooling capacity. I haven't looked at their methodology (not that they post it), but given the dearth of data here, it's going to be hit-and-miss.
Perhaps a bigger concern (though, maybe not) than noise, is the unit failing prematurely. If you oversize the AC unit, you have to worry about short cycles and the motor dying prematurely and such. If you undersize it, the motor will run continuously, potentially failing early as well.
If you are talking about central AC units, you can make sure the outdoor unit is free of debris and such, which can contribute to noise. But most outdoor units are quiet enough that they don't both people inside the house.
Larger computer fans emit less noise because they spin slower while moving the same amount of air, as compared to a smaller fan. If they spun at the same speed, they would emit more noise than the smaller fan. AC units work in an entirely different manner, so one should not expect a similar principle to apply.
