The HD595 has the exact same kind of sonic signature (neutral, with deep bass, a great midrange, and slightly on the bright side, good for rock and techno lovers but definitely ok with classical music and jazz).
What makes them different is the HD595's highs sound a lot less tinny, the sound is a bit fuller, bass is more articulate, and the mids are a bit more detailed.
The highs are the single biggest improvement; the 555s are a bit more distorted and definitely have characteristics of cheaper phones. 595s dont have much of this at all.
Either phone is worth buying one hundred percent, but I guarantee you'll benefit if you buy the 595 over the 555. If you want a more neutral sound without as much of an emphasis on highs the HD580, 600, or 650 is your phone. The 580-600-650 really needs an amp, period, and a great source, period, and a great set of recordings, period. The 515-555-595 don't, however, and sound better on lesser equipment compared to the HD580+ series.
Cheers,
Geek
Cheers,
Geek