It's unfair to compare European and American heat pumps. The market is much larger more mature here in Europe and the differences in how you think about heating are large. I've heard that american heat pumps are quite noisy, mainly because you place them away from the living area (there's no reason to lower the noise). In new-built houses here in Europe they are most often placed directly within the living area so the heat pumps must be very quiet.

Disclaimer: I work for one of the heat pump manufacturers in Europe (albeit with connectivity solutions and not actual heat pump technology)

Depends how much you pay. The last time I looked a simple air to air pump the cheapest was 31dB and the most expensive was 21dB. So very quiet indeed.

About one in five houses have heat pumps where I live (about 40km south of Oslo) and I can hear them humming as I walk past but of course they are not the latest models. Still they are orders of magnitude quieter than the units outside the flat I rented in Cary, NC ten years ago.

Air-to-air pumps will probably always make some noise because air has relatively small thermal capacity, requiring relatively big air flow in order to transfer any meaningful amount of energy.

There also exists heat pumps which transfer heat to water-based central heating system (radiators / floor heating), eliminating the noise issue. The heat source can be either outside air or liquid circulating in soil/well (possibly supported by solar). All these combinations are relatively common in Scandinavia, air-to-air pump being most popular because of quick ROI (small initial investment) and easy retro-fitting, althought practically all new houses are built with water-based central heating (the heat source being either of electricity/solar/wood/air pump or any combination).

I would also like to hear about heat pumps. A lot of information is either white papers or scienceless consumer information, with no middle ground.