My mum has a large Mitsubishi outdoor unit and when it's running it sounds like a noisy dump truck idling just outside the room - in fact the first time I heard it I could not understand how a truck could be so close to her house until I went outside to see what the noise was! Although Mitsubishi markets into domestic applications, their stuff is better suited to commercial and industrial applications where noise pollution isn't such an issue.
Sound doesn't just travel straight through the fence; there are many flanking paths over the top of the wall from reflections from the neighbour's wall and eaves above the fence, etc, plus at the top of the fence sound diffracts (bends) over the top. A solid heavy barrier like a brick wall will work best and make sure there are no gaps, e.g. at the bottom. The higher and longer the wall or barrier, the better. Have a look at the walls in front of houses on main roads which have been widened and owners offered noise protection.
I've recently returned from Japan where all of the outdoor units are virtually silent, even though they are the same brands eg Mitsubishi, Panasonic, Fujitsu, etc, so it must be something to do with a lack of performance standards in Australia. Noisey units are cheaper to make.