Joyce do I take it that your hedge is along the front of your house, and the neighbour's hedge is along the front of their house? If so then they really are two separate hedges - you can't expect them to be the same.
Do you paint and decorate your house to match theirs? Of course you don't, any more than your garden planting matches theirs.
They are two different properties - you cannot control what your neighbours do - enjoy your garden and enjoy the difference