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it is possible that the wire you got is of lower quality. it all depends on the quality of the smaller wires and connectors that they used to make the cable itself.
in the world of an analog, yes. but HDMI is digital. the picture quality cannot be degraded by the cable at all. either the cable will produce a picture, or it wont produce one at all, theres no quality differences.
if you know what HDMI on the xbox looks like (and if you dont, you may of just had wishful thinking hoping that the graphics would improve, which it will only improve the black and white colours, and the sharpness) then i would put it down to your TV and/or to what resolution you have the xbox set to.