It's funny, I personally find Zooey's voice much better when she sings jazz than pop. I can't take her seriously as a jazz singer, but as a throwback to some minor starlet of the golden age competently singing a sweet little ditty in an exaggerated Hollywood twang, it works for me. And though I actually love her pop songwriting, her voice frustrates me in her own songs. I feel like she struggles with the shorter phrasing of pop - her voice just so often sounds cut off prematurely and not in control. She falters quite audibly on some notes and sounds out of breath at the end of some phrases. But mostly she sounds inconsistent, often within the same line. There is this unevenly loud and soft fluctuation that is a bit hard on the ears.I feel there is something about her nasal voice that just can't get much power or feeling in the short bursts pop requires. Whereas with jazz, though not brilliant, I think her voice sounds more even and in control.
I'm kind of surprised she considered being a Broadway songstress, though it makes sense of my feeling that she overestimates her skill as a singer. Ultimately that over-confidence ends up hurting her pop. So many of her songs would sound better without her shaky vocals showcased quite so upfront in the mix. The songs are so good and I just think they could sound that much better.