Hi Mel,
It's a little difficult to understand the exact layout of your home and your neighbor's house. It would be better if you sent a picture.
The way I understand your description is that the house next door is set back 15' further than your home, and it is 8' away.
A landscape design will always look prettier and softer with plantings in front of a fence. Add some masses of shrubs and perennials. In addition, an ornamental tree will enhance the look further.
You can even add a trellis with some climbing plants in one area. This will add some additional interest.
