Your observation was pretty much on point. If you play a BluRay disk into a new TV, it's obvious if it has 1080p.
Otherwise, I too don't see the difference in 1080i and 720p systems. For a 1080i system to work it has to have more pixels than a 720p TV. But even on a good 1080i
LCD or Plasma something happens that maybe hard to follow depending on your background in TV that does render little difference.
On a tube TV back in the 480i days. The station transmitted 60 fields a second, making that into 30 frames per second. Each field had every other line in the image. The persistence of the phosphors in the tube would "hold" the previous field of odd lines while the next field of even lines were swept to the screen. Your eyes and the tube would "merge" the two fields into a frame (all 480 lines), which is what you would perceive, not the individual fields (of 240 lines). (Yes those that really know TV some of the lines are used for other things, but keeping it simple, ok?).
Now bring in the
LCD TV. The
LCD turns off and on rapidly and has no persistence to speak of to the human eye. This is not a problem with 720p. And standard that is a p, means progressive scanning and there are no fields, only frames. Or you could say the fields equal the frames. So viewing a 720p image on an
LCD TV that is 720p, you will have 720 lines top to bottom on the screen. There is no interlacing of odd and even lines. LCDs were made for progressive scanning.
Now lets push a 1080i image on a
LCD screen. LCDs won't persist and your eye would see flickering if they tried to do that. So inside the TV there is a circuit that takes, the odd and even fields of any i type signal (480i or 1080i) and converts them into progressive scans. So even though 1080i has 60 fields a second, the circuit in the
LCD TV converts that to 30 frames a second to show on the
LCD.
Then if you buy a 1080i TV, because it's
LCD, it still can do interlace. So it too must convert the 1080i to 1080p, but with half the resolution of real 1080p to show on the screen.
So really unless you have money to burn, to me it's not worth buying a 1080i TV. Now upgrading to 1080p if you have a Blu Ray or other 1080p source then yes, that is worth the money if you want to spend that much for that resolution.
So your eyes told you the story I just explained technically.