It makes sense to you to broadcast the same frame twice for progressive?
Look:
480i -> 480 lines of resolution drawn odd lines and then even lines at 60Hz, which is 60 fields per second, totalling 30 frames per second of data (not actual frames)
480p -> 480 lines of resolution drawn one frame at a time at 60Hz, totalling 60 frames per second of data.

Of course the mpeg-2 compression allows for a variety of different formats, but as a general rule if your HD station is progressive, it's at 60 frames per second.

See below for ATSC's standards. (AKA the horse's mouth)

http://www.atsc.org/standards/a_53c.pdf

Page 29 -> 36. You'll find of interest Tables A1, A3, and A10. You'll notice there are only three different line resolution for input formats, and also that 59.94/60Hz frame rate. I assure you all 720p stations in my reach _are_ broadcasting at 60Hz progressive which is 60 frames per second. Also you see that interlaced and progressive video formats reference the same line count SMPTE standard.

Less engineering oriented here:
http://www.atsc.org/standards/a_54a.pdf

Pages 24 and 25, Tables 5.1, 5.2 and section 5.2.1.2 Those picture rates should be a clue. As you can see the subject is much more complex, however in reality stations are broadcasting at 60I or 60P.

A still picture at 1080i and 1080p should be identical, if not, you've been ripped of by your set manufacturer/salesmen/etc. Even a set capable of drawing 1080 lines it may not actually be able to display it because the beam size is too large to allow for 1080 distinct lines. Try writing a letter by hand with a super-magic-marker.

http://electronics.howstuffworks.com/hdtv1.htm
"Progressive scanning shows the whole picture, every line in one showing, every sixtieth of a second. This provides for a much smoother picture, but uses slightly more bandwidth."

As for one being better than the other, the both are - for their respective uses which becomes clear when you understand the formats.