Ask Mr. Smarty Plants

In fairness, your question should probably be directed to Mr. Smarty Engineer, since the problem really is an engineering one.  However, Mr. Smarty Plants happens to be aware of harmonic sound propagation by motors and pumps and so he will try to help.

In no way will vegetation help solve the problem, unless in the very unlikely scenario you were to mount the neighbors' pool pump to a large tree.  If your fence is a wooden one, your first inclination to place sound-deadening materials on it wasn't a bad idea, since in certain situations, a wooden fence might act as a sound board - think of a violin, cello or guitar body here.  But it's far more likely some other structure is acting as a sound board and amplifier to propagate the sound vibrations of the neighbors' pump all the way to your unhappy eardrums.

The best -- and happily, the simplest and cheapest -- solution is to mount your neighbors' pump on rubber motor mounts.  Pretty much any pool equipment supplier will have them and they are relatively simple to install.  Finally, your neighbors might want to remount their pump on rubber mounts anyway since rubber mounts will also reduce the likelihood of vibration-related damage to their plumbing and other components.