It is easy to see that both Paillier and Goldwasser-Micali are homomorphic addition schemes and are secure, but what would be the advantages of choosing one over the other?

With Goldwasser-Micali, you can, given $$E(x)$$ and $$E(y)$$, compute $$E(x \oplus y)$$ (where $$\oplus$$ is exclusive or)
With Pallier, you can, given $$E(x)$$ and $$E(y)$$, compute $$E(x + y \bmod n)$$, where $$n$$ is a large integer; this implies that, given $$E(x)$$ and $$k$$, you can compute $$E(kx \bmod n)$$
• @DanielK: that is correct (unless you mean addition in $GF(2)$, which is xor…) Feb 14 '20 at 15:46