Steam at the same temperature with water, contains more energy than a sample of the same mass of water due to the following reason:
The main reason for this is due to the fact that steam has a higher latent heat of vaporization. Latent heat of vaporization refers to the amount of heat energy required to change the phase of a mole of a liquid to gas.
The amount of heat energy in joules required to raise 1 gram of steam by 1 Kelvin is higher than that required to raise the same mass of a liquid by 1 Kelvin.
This means that one needs more energy to raise the temperature of steam as compared to the amount of energy required to raise the same amount of water to the same temperature - the steam will absorb more energy to get it to the same temperature as water.
The result is that the steam would have more energy than water at the same temperature; for instance at 373K