If I pay for the fence because the neighbour doesn’t want to. And I arrange it all, collect the timber, and spend two days putting the fence up, I’m sure as hell going to get the “good side” facing me, and he can have the side where you can see all the posts.
If you are doing it because he doesn’t want to I’m assuming you mean it is his responsibility or it is shared responsibility and you are taking the full financial and time faff hit on their behalf. If that’s the case you have every right to have the good side, not just ‘moral’ right.
If the fence is your sole responsibility (i.e. you are not doing it because your neighbour doesn’t want to but because you have to and they don’t) you are meant to have the ‘bad’ side. I’m assuming this ‘rule’ (again not sure if it is law) is so people don’t put up god damn awful constructions in the knowledge that the neighbour cops the worst of it. The upside to this is you should get the ‘best’ side of the fence your other neighbour is responsible for. I guess with shared responsibility fencing all bets are off and I’ve no idea who gets what (am assuming the person who goes to the trouble of organising or doing the work gets the best bit by default).
People who say this have obviously never seen a set of deeds. In most cases, especially Victorian era houses, they say pretty much bugger all.
All of our houses we have owned have had the responsibilities clearly marked. One of the houses was a couple of hundred years old too. The comment above about people have not seen deeds is not strictly correct although I don’t doubt there are plenty of properties where this is the case.