Microscopically, temperature is related to the average kinetic energy of a system in thermal equilibrium. Both LIQUID water and GASEOUS steam can exist (independently) at a temperature of 100 degree Celsius (say during boiling). But surely, steam has higher kinetic energy than liquid water. How then, can they be said to have the same temperature?
There are some intricate concepts here that I can only begin to explain.
To start with - in liquid water there are strong intermolecular forces. In order to water to turn into steam, these forces have to be overcome. The work done is the latent heat of evaporation. But the question is - does it follow that the molecules in steam at 100°C have higher kinetic energy than molecules in water? Or is the difference just in the intermolecular bonds?
The specific heat of water at 100C is 4.219 kJ/kg/K; for steam, the corresponding number is 1.890 kJ/kg/K. That's very strange, but explained here. Basically, as water is heated and the molecules move faster, more and more of the hydrogen bonds are broken; this requires a fair bit of energy - it accounts for more than half the heat capacity of liquid water.
However, both in liquid water and in steam there are five degrees of freedom (two rotation, three translation) which store the kinetic energy. And there's no reason to believe that they have a different amount of energy / motion when they are at the same temperature. That doesn't mean they don't have different energy content - but you specifically asked about kinetic energy content.
Because steam has latent heat in it. Latent heat is required to break the attractions in water and convert it to a gaseous phase. So gaseous steam seems to have a higher kinetic energy.
EDIT: The earlier answer was unclear and its presentation was misleading. The energy of the system comprises of potential energy terms, which are attractions between the water molecules, and kinetic energy terms. Now the difference between gaseous and water steam is although they are both at same temperature, gaseous steam has latent heat added to it which breaks the attractions , i.e the potential energy terms. Temperature is the measure of the average kinetic energy and therefore it remains the same. Steam doesn't have a higher kinetic energy but a higher total energy.