OverTheAir reception of local digital stations will always give you the highest quality picture, providing you have an antenna strong enough to get a signal over the minimum threshold.
Most cablecos, including Cox, use either statistical multiplexing or rate shaping to strip bandwidth out of the full HDTV signal. DirecTV and Dish do stat-muxing plus resolution reduction to fit more HD channels onto a sat transponder. Example: WCBS-DT from NY broadcasts 1920 x 1080i OTA resolution (a little over 2 million pixels). DirecTV downrezzes this to 1220 x 1080i, which is only 1.3 million pixels. On many TVs, you won't see the difference, but on a larger set that does full HD resolution, the difference is noticeable.
A local broadcast station is allowed ~19mbs of bandwidth to do whatever they want with, as long as they provide at least one channel of minimum 480i resolution. To do full 1920x1080i resolution (which CBS & NBC broadcast in), they need the full 19mbs to do it right, so originally stations planned to either send out ONE channel of full HD or multicast several channels of lower resolution within their 19mbs of bandwidth.
But recently, many stations have begun to multicast one or more 480i sub channels, in addition to attempting one 1080i sub channel. The results are not always good, especially if there is any fast motion or scene changes in the program.
ABC & FOX broadcast at 720p resolution, which is less bandwidth intensive than 1080i. So they can usually get away with one or two extra multicast subchannels without much picture quality degradation.