I have both a heat pump and resistive heating in my house. The compressor goes outside the house so you never hear it (and it's not particularly loud, just sounds like a quiet powerful fan). The indoor split units, as they're called, just blow air over the coils. The fans are very quiet, quieter than a typical standing fan or an A/C vent blowing air.

Resistive heating is usually much quieter, however it can make annoying ticking sounds as the metal expands against the wall, or an annoying electrical buzz as the power is cycled on and off, multiple times a minute. This happens even if they're installed perfectly, houses and walls move over time.