They are quite different, but also pretty similar.
Zim is loud and energetic, always moving and always scheming. Gaz is quiet, introspective and a lazy fuck. Even when something gets her going, she'll still be very quiet.
However, they both hate Dib with passion and enjoy seeing him suffering. Getting a bit Freudian here, Gaz is a daddy's girl, and Membrane is a man of unconventional genius. Zim is also an unconventional genius.
You also have the misanthropy in general.