A Bambi, with its fridge compressor style enclosure, is probably the quietest closely followed by the similar industrial rated compressor and reservoir units from other makers such as Jun-Air. to name one I have personal experience of.
But they are expensive.
The affordable twin exposed diaphragm compressor beasts, like that one, are rather noisier than the better versions of the small suitcase stye compressors. My FIAC Compact 106 claims 57 dB but FAD is low at 3.5 cfm. and the tank is small. Don’t really hear it start and stop when running my Bijur mist style lubricators on mill and lathes.
But the suitcase compressor market is total minefield with some remarkably noisy devices sold on the basis of small size only. Some are little more than uprated car tyre inflators and really should come with ear defenders. Brand being no protection. Looking at you Makita and the normally reliable LiDL Parkside offering proved far louder than friend could tolerate. Funnily enough the Parkside one made a one time only in the middle of LiDL. I suspect my friend wasn’t the only one to sling it back same day.
An oldie, but goodie, is the baby Hydrovane PR303E unit made for Binks Bullows continuous air feed compressors. Possibly the quietest of the lot due to the near continuous airflow and, apparently, built to exceed the 100 years and a day life of Wendell Holmes famous One Horse Shay. If you want one prices are all over the place from daydream £350 + on E-Bay to £20 at the bottom end of Facebook marketplace, back of a charity or used tool shop. Need to DIY a tank though and only 40 psi or so.
Fitting a decent air filter box with reasonable volume inside damps out the induction pulses inevitable with a diaphragm or piston compressor which makes a useful reduction in noise. Steal the airbox off a small car or adapt a (tubular?) filter. OK it’s a much bigger unit but many years ago I put a SAAB 9000 air filter between the arms of an Atlas Copco KE series Vee twin compressor which seriously reduced the noise. Memory suggests down to little more than twice as loud as the Hydrovane that replaced it.
Clive