Is your TV calibrated specifically to both players? You really need to do this before comparing different DVD models or wires. Usually the Xbox is not considered near the top of pic quality.

What is your budget wire? For video it isn't too hard to see differences between wires if they are not of similar construction. Or at least if one of them has poor specs for video. You can't really beat the types of cable that BJC makes, but that doesn't mean your current one is worse.

With DVI, you are skipping 2 conversion stages. To use component it has to convert digital to analog in your DVDp or HD box, then back to digital in the DLP TV. Usually one would expect that to damage the signal a bit more than the straight digital connection. But there are other issues like the sparklies you mentioned, so it is never quite so cut and dried.