It's BOTH.

To be a great composer you have to have BOTH nurture and talent.  When
I say nurture I am saying you have to be exposed to music.  It doesn't
necessarily mean that your parents had to force you to study music.(My
family could care less for my performing capabilities but I think I turned
out okay) You also have to have a love for music as well.  I don't see how
anyone could agonize over writing a whole symphony and not have a love for
the music.  The composer can have great talent, but no love for music.
Therefore he or she will get lazy and will never produce anything worth
listening to.

Jeremey