Does saying どこの出身 sound any different than saying 出身はどこ? More generally, does
adnominally modifying a noun have some other feeling associated with in? That
is, in comparison to just using a standard subject-predicate construction.
(I'm not sure that that is the right descriptor for the second phrasing.)
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2014-05-27T17:01:25.283
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meaning
出身はどこ vs. どこの出身
To pick some examples:

  * 何を食べたい？ 食べたいものは何？
  * 何を見た？ 見たものは何？ 
  * どこに行った？ 行った場所はどこ？ etc.

Did I get the idea correctly? If so, then I would argue that the difference in
feelings of those two are rather subtle/insignificant. If you use them in
speaking, your tone of voice would be more influential than the different
construction of these phrases.

That said, this subtle difference does exist --- the latter phrases are more
interrogating --- because questions in Japanese, in practice, are indicated
almost solely by the intonations (i.e. higher pitch to the end) rather than
grammars, so the word/phrase that has such a pitch is emphasized as a core of
the question.

P.S. as istrasci mentions, どこ出身？ is a common very casual way, but 出身どこ？ is as
common as that.
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(The following is based on something I originally worked out for myself. There
may be other views but it seems to hold.)

As the first answer says, the difference between these two expressions will
largely depend on context - the situation, how they are said etc. - and the
nuance is probably slight but worth understanding.

The particle の is often used to replace が and therefore I would suggest that,
**to the extent it exists** , the difference between 出身はどこ and どこの出身 is
similar to the difference between using は and が but with the some provisos.

As が places emphasis on what comes before it and は places emphasis on what
comes after, and you have effectively reversed the word order, you could argue
that the emphasis on どこ has not substantially changed, even if we extend these
expressions into more "complete" formal questions:

> 田中さんはどこの出身でしょう？  
>  田中さんの出身はどこでしょう？

The main proviso is (as pointed out in the response to the previous question:
[noun + の +
adjective](https://japanese.stackexchange.com/questions/14056/noun-) ) that
replacing が with の softens the impact, and places emphasis on what comes after
の.

You could analyse this further but given the two expressions are not that
different, I would suggest stopping here and moving to look at the difference
between between は and が in more extreme and varied cases. There are several
explanations. I find the one by Kuno, cited on this site the most useful.
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