> Is there a reason why […] is a better translation […]?
What do you mean with "a reason why"? From a synchronic or a diachronic point of view? Yes, there are reasons that linguists can provide. But for the mere layman, it will simply be weird to encounter such an utterance, full stop. Not that your question is non-sense, I would rather simply expect most people to be unable to tell you why despite they know it sounds weird.
> I know it's just a word-for-word translation, but the latter seems more natural, and the former unnecessarily verbose.
What you mean with "seems more natural", is that it sounds closer to what you are accustomed to in your own language. French is generally more verbose than English, especially in usual written form.
Now, as your "why" is nontheless completely legitimate, here is one explanation .In the case of "sa bibliothèque et la sienne", unlike in English which insist on the possessor (his/her takes the gender of the one who owns the object), French insists on the possessed (sien/sienne takes the gender of the object which is possessed, and every substantive have a gender). So would you translate "her library and his" in the same way, you would end up with the very same translation "sa bibliothèque et la sienne". On the other hand "sa bibliothèque à elle et sa bibliothèque à lui" would preserve the information of who owns each library.
Would you really mind to comes that is as close as possible to the original prosody, you might use "sa bibliothèque à lui, et elle la sienne."
What do you mean with "a reason why"? From a synchronic or a diachronic point of view? Yes, there are reasons that linguists can provide. But for the mere layman, it will simply be weird to encounter such an utterance, full stop. Not that your question is non-sense, I would rather simply expect most people to be unable to tell you why despite they know it sounds weird.
> I know it's just a word-for-word translation, but the latter seems more natural, and the former unnecessarily verbose.
What you mean with "seems more natural", is that it sounds closer to what you are accustomed to in your own language. French is generally more verbose than English, especially in usual written form.
Now, as your "why" is nontheless completely legitimate, here is one explanation .In the case of "sa bibliothèque et la sienne", unlike in English which insist on the possessor (his/her takes the gender of the one who owns the object), French insists on the possessed (sien/sienne takes the gender of the object which is possessed, and every substantive have a gender). So would you translate "her library and his" in the same way, you would end up with the very same translation "sa bibliothèque et la sienne". On the other hand "sa bibliothèque à elle et sa bibliothèque à lui" would preserve the information of who owns each library.
Would you really mind to comes that is as close as possible to the original prosody, you might use "sa bibliothèque à lui, et elle la sienne."