Let us first examine the ideal case, where we ignore air resistance.
Without Taking Air Resistance Into Account:
When the stone is traveling upwards, it will go through a certain point A, and will be travelling with a specific velocity. The only force acting on this stone is the force of gravity, and this only depends on the mass of the object. So for the whole process, the stone will go up through point A, reach the top of it's trajectory, and come back down through point A traveling at the same speed it went up with.
Since it is traveling at the same velocity both on the way up and on the way down, the kinetic energy is the same. Now let's look at what happens when we consider air resistance.
Taking Air Resistance Into Account:
In this situation, the stone will go through the point A at a certain velocity, and the only forces acting on it will be the force of gravity and the force of air resistance. When the stone is traveling upwards, the force of gravity is going to be removing kinetic energy from the stone, and the force of air resistance will be as well.
On the way down, the force of gravity will be restoring kinetic energy to the stone, but the force of air resistance will still be acting to slow the stone. Therefore, the stone will have less kinetic energy on the way down than it had on the way up, solely due to the influence of air resistance.