In the MacRumors forums (thread HERE), an interesting discussion has emerged on the visible differences between the two most widely used consumer high-resolution video formats, 720p (meaning 1280*780 pixels) and 1080p (1920*1080 pixels) are visible at all on the iPad 3's screen.
Much as I've already published several articles (see for example THIS) linking to third-party articles (e.g., THIS) comparing the visual quality between 720p and 1080p movies available in iTunes' own store, I've decided to chime in the discussion with my own test images as quite a few people tend to state there isn't any difference to the human eye. Which is completely wrong, assuming you keep your iPad 3 some 30 cm's (12 inches) from your eyes (and not further away) while watching the video. Particularly if you use my windowed Full HD player, which increases clarity even more by not letting the system scale the picture both horizontally and vertically to full screen, eradicating all the fine(st) detail.
The answer to the original question is, therefore, most definitely YES: the difference is obvious even for the non-trained eye and even when letting the system scale the video to full screen. (Actually, as opposed to the 1080p case, I don't recommend using windowed playback for 720p content. The window size would be far too small – only slightly wider (1280 pixels) than half (!) of the screen's width, 2048 pixels. Therefore, I don't release a native 720p player, as opposed to 1080p, where you “only” lose 128 pixels to gain as clear and contrasty picture as possible by not scaling the image to full screen.) In order to demonstrate this, I've quickly generated a 720p test video of my standardized resolution chart. (For this, I've used FCPX. See Section “5. Addendum – how did I create the test videos? + Tips for disabling the Ken Burns effect” in THIS article for more info on how it can be done.) The just-created 720p video file is HERE; the 1080p one I've already used in my previous tests HERE. Feel free to sync both of them to your iPad 3 to see the difference.
I've also made some framegrabs of the two resolution chart videos being played back in the built-in Videos app on the iPad3 (alternatively, you can use any other player using the Videos engine to play back videos). They're HERE (720p) and HERE (1080p). I don't paste them in their entirety as it'd be meaningless to try to demonstrate resolution differences originating from a 2k image in a 600-pixel-wide shot – that is, click the links to see them. I, however, show you some of the most important differences:
Hope the difference in the resolution doesn't need to be explained: the 1080p shot is WAY better, even if you take into account that it's been rendered full screen, where, due to the 1920 > 2048 automatic resolution scaling, its resolution becomes lower. (This is why I've written a windowed Full HD video player not allowing for any kind of scaling, after all.) For example, try conting the number of vertical lines in the 720p shot to the left of the label "10", and do the same to the 1080p shot. Yes, the difference is THAT big.
BTW, I've also created a difference image of the two framegrabs. It's as follows:
(click the link for the full, iPad 3 screen-sized original, non-annotated version! The full-resolution annotated version if HERE.)
As you can see in this (too), almost every part of the image is affected by the difference between the resolution of the, otherwise, same source image. The difference is particularly pronounced in the areas, that is, where lines are so close to each other that 720p can't resolve them as different entities any more, while 1080p still can.
Exactly this is why the areas labeled 6...7 (annotated by rectangles) are the most bright in the difference image (it's exactly the region I've spoken of), while, for example, regions over 10 (annotated by ovals) are almost completely dark because not even 1080p can render individual lines in them any more and, therefore, they're rendered in both 720p and 1080p modes as an almost completely solid, grey area.
Incidentally, it's worth comparing the above difference image to that of the 1920 > 2048 anamorphic video stretching (see THIS article):
(the difference image used in the 1920 > 2048 anamorphic video test)
The video resolutions I've compared in that article were 1080p (1920 pixels) and 2k (=2048-wide video). There, it's the areas bearing the label 10-12 are the brightest (in the 720p vs. 1080p case, they're already almost completely dark, showing neither of the two resolutions were able to render the fine-grained line structure in those areas). Also note that the difference between the anamorphic video and the native 2k one are FAR less noticable than the differences between the 720p and the 1080p ones. This is why the second image is so much darker overall, with far less prevalent bright spots.
You can safely say “well, I still stick to 720p as (very) old movies don't necessarily have the necessary resolution to look crisper in 1080p”. You're definitely right: in those cases, 1080p MAY be an overshot as the celluoid may have aged too much and/or didn't deliver much detail even when it was shot. Also, there are cases where you might not want to use 1080p; for example, when you must reduce (or completely eliminate) the very annoying buffering / pauses during streaming if you do stream the video, even from your home UPnP / FTP / SMB / iTunes Sharing etc. servers instead of playing it back from the local iPad. Also, if you watch the iPad 3 from quite a distance (as opposed to the 30 cm's I've mentioned in the intro), you might not need the extra resolution. Finally, if you don't have a good (or even average) eyesight, you might not see much difference either.
However, in all other cases, you WILL notice the difference.