$\boxplus$- key addition vs $\oplus$- key addition
As pointed out in the comments, one attraction of mixing $\oplus$ and $\boxplus$ is that it makes cryptanalysis harder due to non-associativity. 

The differential properties of $\boxplus$ were analysed here and you can find out more by chasing citations to this paper. Massey's PHT (Pseudo Hadamard Transform) is also of interest and was used in SAFER and Twofish.

In terms of key addition using $\boxplus$, the diffusion is slower than XOR when there is no carry, with no added benefits and that is probably why it is not used widely. And the somewhat annoying fact that during decryption, to undo addition of $k$ you must subtract it.