The bottom line: 1080p has a better screen resolution.
cons: You probably won’t notice much of a difference between 1080p and 1080i because most technology even in the current market is not true 1080p capable.
The technical stuff — What makes 1080p and 1080i different?
1080i screen resolution: Each frame of video is displayed in alternative fields. The fields in 1080i resolution are composed of 540 rows of pixels or lines of pixels running from the top to the bottom of the screen, with odd fields displayed first and the even fields displayed second. Combined, both fields create a full frame every 30th of a second, each frame of which is made up of all 1,080 pixel rows or lines.
1080p screen resolution: Video frames are displayed progressively. This means that both the odd and even fields (all 1,080 pixel rows or pixel lines) that make up the full frame display together instead of being sequential like in 1080i.
Summary: 1080p has a smoother looking image, with less motion artifacts and jagged edges.
Fun fact about 1080p screen resolution:
Your TV (cable) is not 1080p.
Nearly all cable channels send an HD signal in 720p or 1080i. A 1080p TV may appear to scale the image to 1080p resolution but it’s actually not a true 1080p image. Blu-Ray devices are one of the few components that are capable of true 1080p . Components like your PS3 may have a Blu-Ray, but believe it or not most games are also not created in 1080p. Technology has not yet caught up with 1080p, despite the large market for selling 1080p TVs. If you purchase a 1080p TV then you are still ahead of the game, and don’t forget to get your TV Installation mounted professionally by InstallHDTV.com!