I owned the 5C for about a week then did the switch to the 5S. Ultimately, I felt like the 5C was a little outdated compared to the 5S. The 5S runs a tiny bit faster, the camera is a lot better, I LOVE the touch ID and the overall feel of the phone in my hands felt overall better. I also prefer black as my primary color, and with the 5C not offering a black color, getting the Space Grey was a no brainer to me overall.
In the end, they both are GREAT phones, however, I feel the 5S is a bit more superior, and if you plan on owning your current phone for quite some time, I believe you should do the switch and get the 5S.