I did my comparison testing in my office, which has a noise floor in the 30ish dB range. Obviously the more background noise there is, the smaller the differences will be. The low impedance version of the DT880 is intended to be portable friendly, but it demands current and the S9 simply ain't got it. With no EQ or enhancements the 880 had pretty much no bass to speak of, thin, reedy mids, and unrefined highs with no definition or detail. With all of the EQ stuff turned on, the bass was lumpy and bloated, mids were grainy, and highs were splashy, harsh, and overbearing. In either case the 880 was pretty much unlistenable out of the S9. The 250 Ohm version might've been better, I don't know. It would probably require maximum volume to hear much, but the current demand would be lower. The 120 Ohm K601 worked fine with the volume at 75-80%. Obviously the 600 Ohm isn't even worth trying.
That's not to say that the only thing the 801 gives you is a more powerful amp. The DAC section is a considerable step up from whatever dirt cheap crap is in a Cowon or Clip and I heard this with the ES10, even though those headphones have little in the way of refinement and one of the smallest soundstages I've experienced. The S9 has no trouble driving the ES10, and the sound out of the 801 was still better in every way. A better sounding portable like the DT1350 should be fantastic out of the 801. I have not done that comparison, but I found the 1350 to be merely above average out of my S9, and I suspect that they have much more to give than I heard.
If you want to listen on the subway or on a bus, the 801 is silly. I use my S9 and my NC-800s in that situation. I'm not interested in maximum fidelity there, I just want to get rid of as much background noise as possible. In situations where I'm away from my desktop Stax rig but I do want maximum fidelity, that's when I use the 801, and I will soon be getting a pair of LA7000s for that purpose. Driving the LA7000 out of a Clip is just brainless, and making the Clip louder by attaching a TTVJ Slim or ALO RX is not going to catch the 801. Using an iPod into one of the new portable iTransport style devices and THEN into a Slim or RX could very well beat the 801, but I like the one box solution that the 801 offers, as well as the FLAC and APE support.