the difference between 1080i and 1080p is that one is interlaced, one is progressive scan
Progressive scan draws every line, interlaced draws alternate lines, leaving a gap in the middle
It then relies on your eyes to fill in the gaps yourself. It does work quite well, but its generally agreed that interlaced is quite good for stuff BBC's natural world documentary, but terrible for fast paced action like football.
The big question on everybody's lips at the moment is how important is 1080P going to be. Remember that 720P is also progressive scan, and is fully supported by anything sporting a "HD ready" logo - something that nearly every LCD/PLasma has been for at least a year now (with one or two silly exceptions)
There are however, only a few LCDs that support it. Samsung / Sony have a joint venture that does (Sony has the W and X series) and the only other true 1080P LCD i know of is the Sharp GX1 (i think thats the correct model). In Plasma's, theres only one, and its a 50" pioneer and it costs £6000.
So its not anywhere like as standard as 720P. You should be asking yourself the question, can you tell the difference between 720P and 1080P ? as 1080i and 1080p you will see a difference, as one is interlaced one is prog scan. As for where you will see a difference with 1080P over 720P, its generally agreed its only on larger screens above 40"