And that's about all the 1080P Dish would usually have at one time, 4.
Component VS HDMI - No difference for PQ, but if not using HDMI if you have a newer audio receiver will lose getting the best audio from many blu-rays. Optical does not carry some of the newer better audio encoded into discs.
And as pointed out, there is virtually no difference to the human eye between 1080P, 1080I or 720P unless the screen is big enough. In fact even 480 will look the same on a smaller TV. That said, even on 55" TV at more than 7 feet viewing distance PQ will look the same between 1080P and 720P. (I'm leaving 1080I out of the equation - that brings in other considerations and some are debatable as mentioned in the post above - it's closer to 720P than 1080P, either just below or above 720P) Even the new somewhat available and very expensive 4K Tv's - on a 55" you would need to be 4' away to see the difference from 1080P. Note this is all for PQ. Better color saturation in some cases can be seen especially with blu-ray 1080P.
Nothing is widely available that matches the PQ of a good blu-ray disc on a large screen TV.