For the most part, the 360 renders to 720p. The question then becomes, "Which scaler is better looking?" between your two devices. Does the 360 take 720p and convert it better than your display?
We do know that the scalers in the 360 are quite good, but also pretty sharp. So, what you are describing may simply be the aliasing that will sometimes be apparent due to the nature of displaying a 720p source on a 1080p display. If your displays scaler is "softer" than the 360's, then that would explain the lack of fluctuating pixels on the 360's 720p output as the display would be softening the hard edges of aliased 720p, but probably also softening fine details as well.
The static? Well, there lies a problem. If you are describing actual static in the image, then something is broken. More than likely, it's just a bad cable in that case. A cable that almost works.
We do know that the scalers in the 360 are quite good, but also pretty sharp. So, what you are describing may simply be the aliasing that will sometimes be apparent due to the nature of displaying a 720p source on a 1080p display. If your displays scaler is "softer" than the 360's, then that would explain the lack of fluctuating pixels on the 360's 720p output as the display would be softening the hard edges of aliased 720p, but probably also softening fine details as well.
The static? Well, there lies a problem. If you are describing actual static in the image, then something is broken. More than likely, it's just a bad cable in that case. A cable that almost works.