In theory 1080p resolution offers better picture quality than 1080i (read on to find out why), but in practice, it is virtually impossible for an average customer to tell the difference.
edit Display Technology
1080i - Interlaced
1080i represents 1,080 lines of resolution scanned in alternate fields consisting of 540 lines each. 1080i is the most commonly used HDTV format, and has been adopted by most television broadcast, cable, and satellite outlets as their HDTV broadcast standard.
However, since 1080p is not officially part of the FCC's approved HDTV broadcast standards, it is displayed either as a result of video upscaling through a specially modified DVD player, video scaler, or a Blu-ray Disc Player, in combination with a 1080p input capable video display device (such as a Television or Video Projector) OR by on-board video processing within the Display device itself than can upscale all input sources to 1080p.
1080p - Progressive
1080p represents 1,080 lines of resolution scanned sequentially. In other words, all lines are scanned in progressively, providing the most detailed high definition video image that is currently available to consumers.
Differences Within 1080p
1080p can also be displayed (depending on the video processing used) as a 1080p/60 (most common), 1080p/30, or in 1080p/24 formats.
- 1080p/60 is essentially the same frame repeated twice every 30th of a second. (enhanced video frame rate).
- 1080p/30 is the same frame displayed once every 30th of a second. (standard live or recorded video frame rate in the US).
- 1080p/24 is the same frame displayed every 24th of a second (standard motion picture film frame rate).
edit Video explaining the differences