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?
They're both additively homomorphic, but over different groups.
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 $E(kx \bmod n)$
Which is appropriate depends on what operation you need to perform on the encrypted data.
In my experience, we almost always want the operations that Pallier provides.