How to compare security between S-Box and Addition in the block ciphers?
So you have addition with carry bitwise if the sum is smaller than $2^n-1$ 
as well as the subtraction of $2^n$ if the sum is greater than $2^n-1.$

Helger Lipmaa has analysis that is relevant in 
"Efficient Algorithms for Computing Differential Properties of Addition" available at

http://kodu.ut.ee/~lipmaa/papers/lm01/

You can use that work as a starting point.