I am no beech expert, but my experience is that when you get around
to it is a good time , and that is it generally worth pruning both
sides. The reason is that some plants will shoot preferentially
from younger growth, and will break out from older wood only if
most of the younger wood has been cut back.
That can be taken too far, of course ....
Regards,
Nick Maclaren.
If you are suggesting NOT trimming the other side ........ie
your neighbours is the way to go then many would disagree
If its your hedge then good gardeners trim their side and their neighbours