From most effective to least:
- The best method of noise reduction is actually to minimise the noise at source. Have you spoken to your neighbour? Perhaps there is the option of isolating the device from the wall itself, or using a mount with rubber bushes to reduce the transmitted vibrations.
Failing that, the two ways sound will propagate are through solids and through the air. Adding sound proofing insulation will reduce the sound transmitted through the air - but to be honest, your existing insulation in the wall should already be quite effective.
To reduce the sound that is directly transmitted you can add rubber spacers inside the wall, to the connecting joists, stubs etc but this requires taking your wall apart!
So the remaining thing to look at is a sound proofing wall covering, which can be very effective. Some are easily suitable for covering a wall without looking too industrial.