Wouldn't high contrast generally mean more/better data collected? And therefore more flexibility? I thought you could alter down, but not up. (in contrast or saturation)
Usually, particularly outdoors in daylight, the problem you'll face is that the difference between deep shadow and direct sunlight (or other bright regions in the image, like scattered light from the sky) is too much for your imaging sensor to capture. If deep shadows look like saturated black, you've thrown away detail in those areas, most likely.
If your sensor has a wider dynamic range, meaning it can retain all that detail from dark to light, that can make the images seem lower contrast when they're displayed, but because all that information is retained, you can potentially go in and increase the contrast by hand to make an image that looks nicer but retains however much detail in the shadows that you prefer.
What makes it more complicated, though, is that good optics are higher contrast, meaning that the lenses aren't artificially scattering light from bright to dark areas of your image. This kind of scattering, usually called "lens flare," can improve shadow detail but it's unpredictable because it often depends on out-of-frame light striking the lens.
Finally, video cameras usually apply a color correction to the image colors which has the effect of making them more contrasty. This is because taking a direct measurement of a scene's brightness and mapping it onto the range of black to white on a display device would make a picture that were very flat and uninspiring, because the display device can't represent the scene's brightness range.
There is more shadow detail in the iPhone 4S outdoor video. This could mean lower quality optics, dirty optics, a higher dynamic range sensor capturing a broader range of brightnesses (and thus looking more flat), or a different contrast curve applied after capture. If I were going to color correct my final product, that extra shadow detail might be a plus, though if it's a matter of lens flare then it might come and go over a shot as the camera moves, and that's no good.
If I were using the video straight out of camera with no adjustment, the punchier iPhone 5 look is more pleasing to me.
I suspect, like I said before, that it's probably flare from a lens that's been exposed to the elements (at least in someone's pocket) because the sensors and optics on these cameras are not THAT different by spec, and I doubt whomever did the test had a pristine, new, in-box iPhone 4S for comparison. This probably affects apparent sharpness as well.
As for things like tearing, that's been a difficulty with iPhone 4S video from the beginning, and the iPhone 5's better specs seem to help, which is good. I have never found the 4S video very useable, for this reason.
