In our previous house, the fence was OK to look at, but didn't offer enough privacy (as you could see through the trellis on the top of it). We covered it in a layer of marine plywood, which we coated with outdoor paint.
It increased our privacy, but also meant we had something nice to look at, and it acted as a nice backdrop to our plants. Maybe worth considering something similar.
Presumably the fence is also mis matched on your neighbour's side ? As you are now buying the property, would it be possible to come to an agreement with the neighbour as to a colour which you would both be happy with ? If the fence is stained/painted on both sides at the same time, no problems with 1 side looking "off" for any length of time.
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It increased our privacy, but also meant we had something nice to look at, and it acted as a nice backdrop to our plants. Maybe worth considering something similar.
BEFORE
AFTER
As you are now buying the property, would it be possible to come to an agreement with the neighbour as to a colour which you would both be happy with ?
If the fence is stained/painted on both sides at the same time, no problems with 1 side looking "off" for any length of time.