I downloaded the photos and looked at them in a photo editing program, PhotoElements. I didn't compare the stock Turbo camera shot because that one is from yesterday and was taken in different lighting conditions.
Camera 360 looks dark and a bit washed out. Poking around with the color picker tool showed the photo was somewhat flat in color. This was my experience with this camera app with my RHMD. It doesn't render accurate colors. Notice that your wall looks like it's tinted gray. I think to the naked eye it's an off-white, almost ecru color.
Google Camera and HD Camera Ultra have almost virtually the same color renditions. Are they accurate? Only you can say but they are almost identical in the spots I tested. I really can't see much difference between them. The Google camera has slightly more depth of field, whereas the HD Camera Ultra app seems a bit brighter. Noise is about the same in both of them. I guess I'd give the nod to the Google camera app, but barely.
Which shot looks the most like what your eyeball perceives?
Thanks for posting this.