According to this breakdown by Semiconductor Insight, reported by EE Times, the iPhone uses the same hardware audio codec from Wolfson as the last generation of iPods, meaning it should sound similar. However, Wired's review suggests that the audio doesn't go as loud as most iPods, particularly the Shuffle, which could be a real problem if you listened to a lot of Rushover headphones in high school. I'm not sure why that should be the case, perhaps a different audio amplifier?
And many reviewers have noted that the iPhone uses a slightly different headphone jack than the iPod, so it can accomodate a microphone in the headphones (which lets users take a phone call while listening to music without switching out headphones). This means that the audiophile headphones purchased for an iPod probably won't work with the iPhone, although adapters are available.
But it seems like it's reasonable, and people aren't buying iPhone for the audio quality, which can't touch vinyl anyway.