720p is the native resolution of your display (hardware).
1080i is the resolution of the input signal (data).
Your TV takes the 1080i signal and scales it to the native 720p resolution.
BTW, all non-crt displays are progressive.

The various HD channels are broadcast in either 720p or 1080i at the source. Your cable STB or Satellite receiver (the box) will take whatever signal resolution from the source and convert it to the output resolution of the box, be it 720p or 1080i.

Theoretically, your picture should look the best if your STB/Receiver is outputing the native resolution of your display. In reality, some TV's look better or the same in the non-native input resolution due to various processing quirks that the TV does regardless of what you set it at.

Bottom line is experiment and trust your eyes.

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