OK. Look
here and
here.
1080 60i produces 30 full frames per second, as defined in ATSC standards. 720 60p produces 60 full frames per second.
I think we can all agree that what we'd really like to see is 1080 60p, which is not an ATSC standard but would be gangbusters for PQ, but cost twice the bandwidth. This can be done on Blu-ray, satellite or cable, but with today's technology we cannot fit 1080 60p (with acceptable PQ) into the 6 MHz/19.4 Mbps television broadcasting channel used in the US today. Not even with MPEG-4, which also is not part of the ATSC standard.
Interlacing only came into existence because early TVs needed a work around to produce the given resolution of the day, due to hardware limitations. If you freeze frame an interlaced picture that has motion in it, you will see an offset in every other display line (ignoring certain other processing).
But with various conversions, limited source capture (1440, anyone?), processing and transmission, etc etc, there simply is no single answer as to which is better. And as stated, if you have a 1080p set, everything fed to it will be displayed 1080p. Whether your 1080 TV can better convert a 720 source than say, a ViP receiver, is up in the air. There is no native pass thru on any current Dish receiver that I am aware of.