A difference of 3dB is 10x the sound pressure. That is usually, but not necessarily, double the perceived loudness.
Not necessarily double the annoyance because the frequency distributions can be different, and what is in the mix of sound is what annoys us. Fairly loud white noise in carefully selected bands is used to calm people, and mask annoying or distracting sounds, while conversations at 1/100 or 1/10,000 the level of a noise masking device will be annoying if we can understand them and don't like what we are hearing.
Whatever the dB rating measured at one particular frequency (e.g. dBA) you really should listen to the generator to see if the noise it actually makes bothers you.