I've used a Sony RX100 II for a year, until I relegated to backup by getting a housing for my Nikon D810.
I went whole-hog at first, buying the Sony, a Nauticam housing, dual strobes, focus light, and both dome and macro wet lenses. The macro was on a flip adapter so I could shoot with or without it underwater. I used the camera on three dive trips, sometimes snorkeling. I ended up never using the dome port, and my macros didn't come out when I tried that lens. (Probably just wasn't as extremely close as I needed to be.)
Personally, I bought the rig as a step up from Canon point-n-shoots with pop-up flash. Lack of (external) flash was just too limiting after 9 years. Having dual flashes made a huge difference, but then it was a huge difference I was going for. Using the rig without flash would still give plenty of good results, particularly in shallow water.
For video, I used the focus light (V24 Fishlite), but it was too weak for subjects more than 2-3 feet away. I never got the white balance right either, but then I never really worked at video. But in general if you want well-lit video below about 15 feet, you need some serious video lights. The camera will do fine for video without lights, but the colors won't be there.
The Nauticam seems a seriously good housing. Enough so that I got another one for the Nikon.
Sony dive shots, including video, here: http://www.cjcphoto.net/roatan2015/index.html
It's a pretty decent little camera. I found that the menu was hard to read underwater, so I turned the LCD brightness way up. That made the shots look very overexposed when reviewing on LCD, but if you trust the histograms you're fine. I found that I got better results setting shutter priority and locking in a minimum 1/160th speed. Other modes were allowing shutter speed to drop as low as 1/30th, and I got a lot of blurry shots that way.