I touched a little on it in my iOS 10 review, but Ben McCarthy — the guy behind Obscura — wrote a great article for iMore about the increased range and depth available when shooting RAW:
In all these tests, JPEG is to the left; RAW to the right. Directly out of the camera, the JPEG looks a little more interesting: It has more contrast, and there appears to be more detail. The RAW image looks downright drab in comparison.
But as Apple SVP Phil Schiller noted on stage during the iPhone 7 event, Apple does a lot of work to process images behind the scenes using its ISP (image signal processor). It makes the images more vibrant and ready to display on the iPhone’s beautiful screen. But it does mean that the image is being altered as you take it — and that can be a detriment when you want to make further changes beyond what the ISP had in mind.
The built-in camera app has always been my go-to capture app, but ever since Ben sent me a build of Obscura with RAW capture support, I’ve used it almost exclusively. I spent some time yesterday shooting with the newest version of Manual, which also has RAW capture support — not that there’s any difference in the RAW files they create, mind you.1 There’s so much more depth and vitality to a RAW file if you’re willing to spend more time editing it. And, if you already spend a lot of time in post-production, you should be shooting RAW.