The version of Bitcoin that better fulfills the properties and functions of money will ultimately win.
We have an example of BCH, which increased the block size, and was able to process more transactions per second. And they lost. Their chain is still usable, but it is less secure, more open to 51% attacks, and it simply became an altcoin.
but the BIP 110 chain could still possess superior monetary properties
The problem with BIP-110 chain is that it reduces use cases, so how is that "superior"? It only blocks some kind of transactions, which means, that all blocked users will automatically be against it.
could remain more decentralized
Blocking arbitrary transactions is not "more decentralized". Actually, it is still unknown, which scripts won't be blocked by future BIPs, built on top of BIP-110, because that community never stated it.
provide stronger assurance that Bitcoin’s monetary policy would not be changed
Actually, BIP-110 proponents want to deploy next soft-forks, which will restrict it further. Which means, that if you want to "keep things unchanged", then BIP-110 is definitely not about it. Example:
https://bitcointalk.org/index.php?topic=5582070but the BIP 110 chain could prevail in the long term
Both chains will be active, as long as miners will keep mining them. How much you could buy with a single coin, is a completely different question.
That is also why I do not think there will actually be hard fork.
The difference between a hard-fork, and a minority soft-fork, is that soft-forks can be united into a single chain, at least in theory. But in practice, the more blocks are produced, the less likely it becomes. And then, the losing side has to be really persistent, to go through all difficulty adjustments, and bring back 10 minutes per block, because by being in a minority, it will take them some time, to get there.
Anyway, hard-forking is quite likely, because if you have for example 100x slower chain, then what is easier: to keep mining it, and go through all needed difficulty adjustments, or to make a hard-fork, and decrease it instantly, by changing the code?
I look at this issue from an economic perspective.
From an economic perspective, you can have no blockchain at all, and a token, which is traded only on some centralized exchange. And it can even have a significant value. In the same way, you can have highly centralized coins, which can be traded for a lot of dollars, because why not. The price is set only by the buyers, and the sellers, so: how many BTCs are you going to trade for BIP-110 coins? Because many BIP-110 proponents are not willing to put any coins, to support their beliefs, which is quite telling.