Here is my thinking on 4K video. The 8Mpx camera can already is equivalent to a 4K frame. And Apple recently hired that sole developer who wrote a clever app that would allow the device to take something like 10-20 8Mpx images per second. If Apple can use a faster sensor they could probably get that up to 30 still shots per second which would then be 30 frames per second for 4K video.
Something like that. The current 8MP sensor on the iPhone 5s is 4:3 ratio, so the 16:9 area used for HD video is cropped to a smaller area. DSLRs that shoot video do that. To get 8MP from video--specifically 2160p 16:9, they would have to either:
(1) use a native 16:9 sensor 8MP chip, which would crop 4:3 or 3:2 ratio photos to less than 8MP, or
(2) use a 4:3 sensor at greater than 8MP in order to attain 2160p without reducing the megapixel count for 4:3 and 3:2 ratio photos.
"These guys [Apple] are really, really good. This [iPhone] is different." --Mike Lazaridis, RIM co-CEO