Another cop out I'm afraid.
I tried really hard but couldn't chose from the later work of either of these songwriting giants, so I went back to the source.
Both albums are relatively unadorned; Simon's wide eyed poetry was unbridled from the quirky world rhythms and smooth jazz that would inform future recordings, whilst Newman's debut is relatively free of the sardonic, self referential Americana and biography, sans the wonderfully florid Southern orchestrations that would color many of his world weary rants and eventually lead him away from the challenge of the charts, towards a career in soundtracks and social commentary.
Both are captured in the raw with their instrument of choice, respectively acoustic guitar and grand piano; with their artistic characters fully developed: there's no sense of 'work in progress' with either recording; both artists were born seemingly fully formed: Simon all wide eyed poetry, Newman all caustic cynicism, both with an ear for melody and an eye for a heart stopping turn of phrase.
Of their later stuff I love Simon's 'Here Comes Rhyming Simon' which contains the sublime 'American Tune', and I couldn't choose between Randy's 'Sail Away' and 'Little Criminals' so, yup, a cop out, but intimate pleasures both.