I can confirm that this is also very noticeable on the iPhone 6. I've tested this on display models and on my own iPhone 6, and on a friends iPhone 6. All have the same issue.
Best "test" video is this one:
Video has to be full screen (best in landscape), without any controls overlapping the video. You really start to notice that the contrast drops when the white levels change in the waves and in the logo in the bottom left. (Especially starting from 0:27).
This contrast-drop occurs in the safari web-video-player, and thus also in the YouTube app.
This does not happen in other apps, like the photo's app when watching a self-shot video.
Really glad that I'm not the only one noticing this. Everyone I show is like "wow, never noticed it before" but it's annoyingly obvious for me every time it happens.
Sorry to resurrect again, an old thread. Looks like a bit of an epic. Anyway, just viewed the above and there's a definite problem watching that video on my iPad Air 2. Here's exactly what's I think is happening, and why it isn't going away unless a stink is made about it. It isn't a bug, glitch or flaw, and it isn't meant to be a cosmetic enhancement. Maybe knowing the following will make it more tolerable...
The playback software is looking for the brightest pixels in the image. If the brightest pixels are only 50% brightness, then Apple figures it can save some power by dropping the backlight to 50% and simultaneously boosting the digital content of the image by 200%. In theory you wouldn't notice any difference. A 50% grey pixel, will still appear 50% grey: software will double it to 100% full white, and the half-dimmed backlight will effectively drop it back to 50% grey.
In theory that's fine, but if the image is changing, and some white pixels suddenly appear in the video, the iPad cannot display them. The backlight is only at 50%, so to display a white pixel, the software would have to set that pixel to 200%, which is impossible. Therefore a fully white pixel will appear no brighter than its grey neighbours. In fact anything brighter than mid grey cannot be displayed, so you see this effect in the whale video above - all the surf, which ought to be white, appears clamped to a mucky grey.
So at this point, iPad will bump up the backlight again, but slowly, and in the case of the whale video, by the time the backlight comes up, the surf is mostly gone, so it drops again. The rhythm in the video means the iPad is always on the back foot, doing the wrong thing.
It's likely also that Apple aren't looking for the absolute brightest pixel in the frame. They probably consider a few outliers to be reasonable casualties, so it might always be the case the very brightest few pixels are clamped to lower than they are supposed to be. Maybe it's the top 1% of pixels which are clamped, maybe it's the top 10%.
The reason the OP had trouble with black levels, and had more problems on older iPads is likely that the older software didn't do quite such a good job of synchronising the backlight and digital brightness changes. The backlights won't have a linear output curve, so getting a perfect match without wobbling the colours a little would be tricky. Perhaps also the older iPads could not ramp up the backlight brightness as quickly as newer ones.
So it's a power saving feature during movie playback. It's a little sneaky IMO. OLED could fix it. Raising a stink about it might get us an option to disable it.