I may stand corrected, but my intuition from the wording is that the first example comes across as “Can I borrow [this]?” while the second is more like “Is it okay if I borrow [this]?” — that is, mostly the same, but in the second example the emphasis is more on the question of borrowing more broadly (seeking permission for the question), while in the first example the emphasis is on the specific item.
Xて(も)いい is “is allowed to X” – this is the construct you want for asking for permission or responding about permission
Xするのがいい is “doing X is good” – this is generic and can mean a lot of things depending on context
Something to note here is the “の” which makes 借りるの a noun. Here you are saying “Is borrowing good?” as in is the act of borrowing good. Where as the てもいい is directly related to asking for permission.
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I may stand corrected, but my intuition from the wording is that the first example comes across as “Can I borrow [this]?” while the second is more like “Is it okay if I borrow [this]?” — that is, mostly the same, but in the second example the emphasis is more on the question of borrowing more broadly (seeking permission for the question), while in the first example the emphasis is on the specific item.
Xて(も)いい is “is allowed to X” – this is the construct you want for asking for permission or responding about permission
Xするのがいい is “doing X is good” – this is generic and can mean a lot of things depending on context
Something to note here is the “の” which makes 借りるの a noun. Here you are saying “Is borrowing good?” as in is the act of borrowing good. Where as the てもいい is directly related to asking for permission.