In all of the side by side shots, the iPhone 5s is on the left and the iPhone 6 on the right.
Lowlight Indoors (click to enlarge)
There is a bit more variation in the tones in the iPhone 6.
The background on the 5s is a lot darker than the 6 which seems to be picking up the mid-tones a bit better, but it does look a little washed out. I could use the exposure control to adjust that but I wanted to capture without any adjustments.
Because the iPhone 6 shot on the right doesn't show as much contrast the image looks a bit flat. In this case I prefer the 5s.
The crispness on the image in the foreground is noticeable on the iPhone 6.
I read that the new iPhone does a better job with red hues than the 5s, but I didn't find much difference when comparing.
For the image above I tapped the center of the lowest flower as the focal point. Both results are similar when enlarged.
Finally I had some fun with the Slo-Mo Video on both the 5s and the 6. The 6 produces quite an amazing slo-mo effect!
Overall I would say there is a slight improvement from the iPhone 5s particularly in shots taken in lower lighting conditions, but nothing earth shattering. I do like the larger size of the iPhone but a bit disappointed in the new camera. Other sites have reported purple fringing in the corners but I haven't experienced that.
Do you have the iPhone 6 or 6 Plus? If so, how would you rate the camera?