Direct drive versus belt is not the issue. My compressor is quieter than any belt drive I have heard. That is 27 cfm of compressor. There is a huge difference between oiled and oil less.
Your compressor appears to be an atlas copo? We use a similar, but oil less version on our 2000-7000hp gen sets to start them if the customer wants air start. The are just as Quiet as the oil type as a small percentage spec them. There are some belt compressors that are quieter by a good amount. But there are four major reasons your compressor is quieter.
1. I would bet the motor is either 1500 or 1800 rpm? Is it three phase as well?
The non industrial direct drives such as the op has is 3600 rpm. Slower turning makes compressors much quieter. The belt drives that are very quiet use a 1800 rpm motor and the belt reduction is to 650 rpm at the pump.
2. It's industrial and made heavier and with better engineering. This dampens sound that is generated
3. Atlas copo does have one of the best intake filter/silencer I have seen in the industry.
4. I think you compressor is pressure lubed but even if it is not the bearings are of much higher tolerance which helps with noise. Cheap compressors use huge tolerances do to crappy machinery/machinist so the won't lock up. Tight tolerances allow smaller clearances which in turn allows better dampening by the oil film and therefore less pounding.