It’s an interesting question that I think is highly subjective. Exclusivity could also play a part In your ring example. Was the grandmothers ring bespoke? If so, even a replica will still be “two” of a kind and I could see the sentimental attributes remaining. However if it was a mass produced item then the only special part was that it was hers, which the replica has lost.

I personally am OK with digitising photographs, and sometimes even pictures of items, because the memoroes they spark are most important to me, however a physical object definitely does have an extra kick if it’s special enough.

In the end sentiment is not very logical, and I think because of that we can never have a true answer.