Difference between 「～のない～」 and 「～がない~」?


For example, plugging these into Google, I can find stuff like, 自信のない人 and
自信がない人. Or, 愛のない生活 and 愛がない生活. I found a movie called 顔のないスパイ. How is this any
different from 顔がないスパイ?

I've asked Japanese people this, and the only answer I've ever gotten is that
that's a hard one to explain, and that there really isn't much difference
worth noting. I'd like to know the gritty details though, what little nuance
each holds.

I feel like I see this difference with "ない" more than anything, but that could
just be me. I can't really recall ever hearing the opposite, like 自信のある人. Is
this significant? Am I wrong?

Thanks!




The difference between this kind of case alternation mostly appears in the
possibility of the logical scope.

> 三人の学生の買った本  
>  '(three possibly different) book(s) that three students bought'
>
> 三人の学生が買った本  
>  'a single book that three students bought'

And indeed, negation is one environment where logical scope becomes relevant,
so yes, there should be difference when you have negation.

