The difference between 1080i and 1080p is how each frame is shown on the screen. 1080 is the number of lines in each frame (numbered top to bottom). The television (and movies) show many frames a second, 30fps for television and 24fps for movies in the theater. On the television, each picture is made up of lines of brightness and color and lasts a very short time on screen.
1080i is interlaced, and means that the picture is produced on the screen by showing all the even numbered lines from one frame, then going back and showing all the odd numbered lines from the next frame. This means the picture processor doesn't have to handle as much data at one time, and can be lower specs and cost.
1808p is progressive, and means the picture is produced on the screen by showing all the lines of each frame, without skipping odd/even. The processor must handle more information, much faster, and has higher specs and price.
1080i shows only half of each HD frame (odd or even lines), and is therefore said to downscale the frame.
1080p actually shows the whole HD frame by scanning all the lines of each frame.
My opinion is that 1080p is better, though MOST people won't see a difference.