My 5S gyro/accelerometer is off by about 4 degrees or more. Many having this issue!
I discovered the accelerometer and gyro are off by about 4 degrees on my 5S. I tried the level in the compass app and its off. I also tried other apps that use the accelerometer and gyro to level the phone and they all show the same results. I rebooted/restored the phone etc. My ipad and iPhone 5 are level at 0 degrees. I tried many surfaces that I know are level and are 0 on the iPhone 5 and Ipad 4. Some apps you can calibrate the level but its always off by default and there is no way to calibrate it globally. If the iphone is off more then a couple of degrees when placed on its edges games such as racing, xplane etc will drift. On my device they drifted to the right.
I posted this info on another forum and many people are reporting the same issue even worse. One user went into the Apple store and tested multiple 4S, 5 and they were all level at 0. Tested 3 5S's and they were off by several degrees. I got a replacement from ATT and it is off by -1 to -2 degrees when flat but when I test it with the phone on its side it is 0 which I can live with is this is how most games, skymaps are used.
I'm not sure if Apple didn't calibrate these properly before they left the factory or this has something to do with the M7 chip. Hopefully they can fix it with a software patch but since the phones are behaving differently they would need to come up with a user calibrate option or give the Genius bars some low level software to do it. Although 0 is ideal most agree 1 is with in tolerance and is acceptable but 3-6 which many are seeing is not acceptable and impacts apps using these sensors.
Here is a screen shot comparing my 5 to my 5S.
iPhone 5s, iOS 7