Processor Speed: The 5S is Faster. The iPhone 5S has a faster processor than the 5C. The 5S sports an Apple A7 processor, while the heart of the 5C is an A6. The A7 is newer and more powerful than the A6, particularly because it's a 64-bit chip (the first in a smartphone).
Also to know is, are the 5 and 5s the same size?
The iPhone 5s is indeed exactly the same size as the iPhone 5, so existing iPhone 5 cases will fit the new iPhone 5s. Of course, cases for the iPhone 5 and 5s won't fit the iPhone 5c, due to the latter's different dimensions and slightly different shape.
Is the iPhone 5 and 5s battery connector the same?
Anyone that has taken these apart will notice the connection and layout is not the same! iPhone 5 only works with iPhone 5 batteries! However, the (larger capacity) iPhone 5S battery does fit in the iPhone 5C. Actually I think the iPhone 5C has a larger capacity battery than the 5S.