So what can these new DSLR's camera do than video cameras can not?

Keep hearing that DSLR cameras like D4 and 1dx and 5DII etc are the way to go for videography. Please explain why these are better with actual links, if possible, to show what these cameras can do that normal video cameras cannot.

I always thought dedicated video cameras were better - they are certainly much more easier to hold and use and focus like a video camera should (had a Nikon 5000 and 7000 once) - and they were a pain using making video's. Also dedicated cameras have image stabilisers - very useful. So what is this attraction of video on still camera increasing so much?

TK