How does the entropy of steam compare to the entropy of ice?

The answer is; The entropy of steam is larger than because it is more disordered than ice

Entropy is synonymous to the degree of disorder or randomness of molecules in a system. The molecules of steam are far apart from each other and move randomly in the system colliding with each other. Those of ice has less kinetic energy, vibrate more or less in a fixed position in the structiure, and are arranged in a orderd fashion

One of the thermodynamic principles says that the entropy increases when the temperature increases, and we have the relation:

dS/dT > 0.

Now, we know that the steam will have more temperature than the ice, so we can say that the entropy of the steam is bigger than the one of the ice.

You also can see in a more "simplistic" concept, entropy is viewed as the amount of "disorder". Now, then the ice has a defined shape where each particle kinda maintains their position, the case is different for gas (the steam in this case) where the particles are almost free, then in the gas, the disorder is bigger than in the ice, and the entropy is also bigger.