So here's how it sounds with different gear...
Sony D-NE500 PCDP+recabled K240S, street: too quiet. Lacking volume (unsurprisingly). This is mostly the player's problem - the D-NE500 is very underpowered, running on a single AA battery and with a weak headphone out.
AC97 onboard audio+Denon AH-D1000 - rather nice, warmish, detailed, with good bass outline and good midrange texture. But there's that slight thick-packed-"squarish" character to the sound, it's almost Sennheiser/Ultrasone-like. The Minibox-D manages to sound natural and effortless, the FiiO doesn't get the same wide-open space soundstage and effortless sparkling dynamics. It's more like a good player amp (somewhat similar to Cowon *2 players) with more power and body. It does sound somewhat too edgy and lacking treble extension, looks like the FiiO slightly sacrifices spatiality for warmth and naturality for definition.
Cowon T2+AH-D1000: this can get unbearably bassy-boomy at times, but otherwise quite nice. But not natural. The amp's slight edginess adds to T2's slight darkness and edginess, and adds to the lack of harmonics (and hence lack of dimension) in MP3 files. To someone not familiar with the higher-end digital (or analogue) formats, this might be impressive, but the artificiality does get burdening after a while. The Minibox-D has an effortless, smooth, wide-open and powerful soundstage, very natural. The FiiO/T2/AH-D1000 combination is more like a show inside a glass box with square edges - it's transparent, but not very lifelike.
Cowon T2+HC1000: the artificiality is still there, but this is a more lovely combination. The FiiO cures HC1000's dip in low midrange, and HC1000's excellent frequency bandwidth gets a boost from the amp. HC1000 sound like full-size headphones powered by the FiiO; some trebliness is still there, but they fill much better. Some of the edginess is noticeable, but it's not as harsh.
Cowon T2+recabled K-240S: surprisingly well. It's still more artificial than the Minibox-D, sounds like a piece of kit (the Minibox-D tends to disappear almost entirely when playing), but it's a good piece of kit. The Minibox makes the Cowon T2 and lossy format files show their artificiality (the space isn't there, everything sounds flatter than it has to be), the FiiO amp just can't reproduce the same dimension/space as the Minibox. So the lack of dimension in lossy MP3 files isn't as obvious, instead what's still there is brought to focus.