Compressor noise will be a combination of multiple noise sources. Some I can think of are:
1. Bearing noise on the compressor and motor. Shouldn't be a big issue unless they're shot.
2. Air noise. Whooshing & turbulance noise as the air is drawn in.
3. Valve noise. Nasty high frequency, metallic clicking/snapping sound. AFAIK, all normal size compressors use reed valves. Huge industrial compressors are likely different.
4. Vibration from an out-of-balance or worn system. Low frequency, but could excite higher frequency resonances.
5. Random mechanical noises from resonances that are transmitted and/or amplified by the metal mounting plate or the tank itself.
6. Mechanical piston noise as it's scraped up and down inside the cylinder.
Any others?
If you look on Youtube for info on reducing compressor noise, it mostly comes down to "build a better intake muffler" because that's the most effective thing that a hobbyist can do. Assuming that the other parts are in good condition (i.e. bearings and isolation mounts in good condition, fans & pulleys not bent), there really isn't much 'low hanging fruit' to work on. A better muffler would help deal with items 2 and 3 above.
Catalina, your large compressor has the luxury of being fixed so a large muffler has no penalty. Also, the larger pipes will reduce the air noise. It probably requires oil so that might reduce various mechanical noises. The portable compressors have to minimize size and weight so they tend to use the smallest mufflers and pipes they can get away with. It seems like the oil-less ones are the noisiest or most annoying as confirmed by your tests.
I noticed that all the California Air Tools style quiet compressors, even the smallest, are two cylinder, single stage units that use direct drive and have the pistons arranged so that when one is compressing the air, the other is drawing in fresh air. They also state that the lower speed of their system reduces noise levels. The few teardowns that I've seen show that the piston isn't sealed with a metallic ring. It uses a teflon seal. Also, they always connect the two cylinder heads with two small pipes so that air can pass between the input sides and between the output sides. But they still use the same crappy little mufflers that the loud compressors do. Smaller units have one muffler and larger units have two. I've also noticed that the design doesn't scale up very well. If you need more CFM, they use two or three smaller units in parallel rather than one big unit.
The direct drive arrangement means fewer bearings. The teflon seal will be very quiet. The opposing pistons might help cancel out some vibrations. The crappy muffler(s) might be a candidate for an upgrade. The pipes between the heads would allow a continuous air flow in and out without stopping and starting the flow.
The only unique thing I see is the pipes between the heads. Is it possible that smoothing out the airflow with these pipes and the opposing pistons is enough to drop the noise by 20 or 30 dB?? Or is it a collection of small improvements that add up to a big noise drop?
Ed