I interpret that as meaning music that takes advantage of a full range of dynamics and emotions; complex and artistic without becoming obtuse; melodic and pleasant without catering to the lowest denominator. Above all, tasteful rather than bombastic.

In which case I would argue classical is the most consistently sophisticated.

But it's almost an impossible conversation to have along genre lines.

As for favorite jazz tunes, I don't know where to begin, but may I recommend the great Slim Gaillard: https://www.youtube.com/watch?v=ntUNRiC5-z0 - not what I would call sophisticated, but I love Slim.