PS3 uses HDMI which might be higher quality I'm not sure what my TV supports or what's the native set. But I do know that for a 360 1080i is max and p requires the VGA cables that are 20-30 dollars. After buying these cables you'll be less then satisfied. The colors don't come out as vivid at least on my Sony. So 1080i is great and you should just settle for that.
Personally although I have have a 1080 TV I didnt' buy it to expect a 1080 signal but actually 720 signal or whatever the standard HD signal is overall. My eyes can in fact see the pixel differences between 720 and 1080. At 1080 the 720 and 420 signal will show a sharper image with my eye sight. I bought 2 versions of the Sony LCD one being 1080 and the other being 720 with the intentions of sending one back as I tested them with my Dish Cable Networks. Which actually did not happen
and I ended up exchaning for a bigger version of the same screen and keeping the 2.