I'm finding it hard to visualise the fence in question.
Here in Australia if a fence needs replacing both neighbours pay half each - and of course, have to agree on the sort of fence ( within their council regulations)
I guess if one side was deemed the bad side, they could agree that neighbour pays bit less.
If a fence doesn't need replacing but one neighbour just wants to change it they pay for it all and would choose which side faces whom.
Here in Australia if a fence needs replacing both neighbours pay half each - and of course, have to agree on the sort of fence ( within their council regulations)
I guess if one side was deemed the bad side, they could agree that neighbour pays bit less.
If a fence doesn't need replacing but one neighbour just wants to change it they pay for it all and would choose which side faces whom.