If a liquid and a solid are at the same temperature, do they have the same kinetic energy? If you have two different materials at the same temperature but are at different states of matter, do they have the same amount of kinetic energy? 
 A: Within a regime where the equipartition theorem provides a good description of the kinetic degrees of freedom in a material (generally this will mean at relatively high temperatures) each atom will have a mean kinetic energy of $\frac{3}{2}k_BT$, regardless of the state of matter. More generally, however, you would not expect there to be a general relationship between the kinetic energy and temperature. In particular in a solid at at low temperatures, where it is necessary to take account of the quatisation of atomic energy levels, the equipartition theorem will not hold.
A: assuming you mean a solid and liquid of different (has to be different) materials.
Temperature is a measure proportional to the average kinetic energy of each particle. So if we keep the number of moles (molecules) the same in the solid and liquid in question, then theoretically yes.
But we can't ignore the chemical properties of the substances (interactions between molecules) if we're to be realistic. I'm guessing that in most solids kinetic energy is transferred by electrons more than anything. In metals the atoms also vibrate but what can we say about the storage of heat energy in a macromolecular structure like silicon dioxide? It's an interesting question but all I can say is that it is true for ideal gases of any kind. That is, if two samples of ideal gases are taken with the same number of moles, they both have the same energy. I cannot answer you're question for liquids and solids, but there is probably no simple description of how it works.
