My understanding is that OTA HDTV is actaully uncompressed, which means you get the best HDTV picture quality when receiving over the air. Cable, uVerse, DirecTV etc all compress their HDTV signals resulting in far more artifacts and pixelization. It is far more noticable when you have a 120 inch projector displaying a football game with lots of moving images etc.
If your station is not broadcasting any subchannels it's a VERY nice signal. (It's still compressed with MPEG-2, the raw bitrate of a 1080p video is over 1Gbit/sec)
Unfortunately most channels in my market are sending 3-4 subchannels which knocks down the quality of the primary. AFAIK only Fox broadcasts a single stream (and football looks pretty freaking great there).
Yes, the cable and dish operators recompress the MPEG-2 stream into whatever they are broadcasting and they do it at a lower quality to cram more channels into their pipe.