I don't think the slope would prevent borders. I'm with mashton - some nice wide borders with shrubs and herbaceous plants would be as good or better than extra fence covering.
Having said that, neighbour noise would seem to be pretty much a fact of life unless you live in a castle / stately home.
I'd just leave them sloped. I wouldn't strip the whole lot in one go, though as that could lead to some soil washing off in heavy rain. Maybe do a couple of 2m length on each side at a time, and build it up.
Once your plants are established, they will stop any risk of run off [monsoons excepted!]
I don't think the slope would prevent borders. I'm with mashton - some nice wide borders with shrubs and herbaceous plants would be as good or better than extra fence covering.
Having said that, neighbour noise would seem to be pretty much a fact of life unless you live in a castle / stately home.