Certain genetic diseases would function differently. In real life, men are heterogametic (they have one copy each of two different sex chromosomes, XY), whereas women are homogametic (they have two copies of one chromosome, XX). This gives two vectors for genetic diseases that affect men more strongly than women. Obviously, harmful genes that are on the Y chromosome don't affect women at all, and harmful genes that occur on the X chromosome are less likely to affect women because they are often recessive. In women, a healthy gene on the other chromosome will override the harmful one. In men, there's no second copy to fall back on, so the harmful one is always expressed. This also means women can be carriers of the disease (having the gene, but no symptoms), whereas men must always be either symptomatic, or free of the disease.
With a ZW system, this is exactly reversed: women must be heterogametic ZW (so that they have a copy of each chromosome to pass on to their children) whereas men are homogametic ZZ. Therefore women would have the same vectors for genetic disease that men do in the real world. Likewise there would be genetic conditions known for being latent in men, but expressed in their female relatives.