Well, the headaches are because you're basically looking at a strong light source that flashes 60 times a second. A CRT screen has phosphorous stuff that lights up, and at 60 hz, it's got enough time to lose it's bightness considerable, before it's lit up again. At higher refresh rates, there's not enough time for the screen to lose it's brightness, resulting in less strains for your eyes. This is because the photoreceptive cells in your eyes are subject to a much steadier flow of photons.
Our TVs are interlaced however, meaning there's one full frame per two refreshes, so the effective framerate is about half of the refresh rate. However, HDTV can run in progressive scan mode, meaning you actually get 50 frames per second. Of course, this is more than our eyes *need* to get a decent impression of motion. The idea is however to make whatever's on the TV move as close to the real world, because our eyes are used to an even higher degree of smoothness there. Even 1000 frames per second wouldn't cover all the movement in the real world.
Anyway, I think the reason why we think Tidus looks like he is walking on on the moon isn't because one technology is superior or inferior. It's more because humans are very good at "everyday physics" and instantly notice when something in the natural world is off or wrong. In this case, the conversion from 60 to 50 hz means the game runs at 24 frames per second instead of 30 (or 29.9 actually!). Because S-E didn't speed up the animation, this results in every animation in the game running at about 80% of the normal speed.





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