It is zero, because kinetic energy is the one associated only with an object in motion. It is maximum just before it touches the ground. And once it reaches the ground, most of the energy is perceived as sound, lost as heat and some as stress, which causes deformation of the body. If the body can't sustain the stress on its impact with the ground, it breaks.
Potential energy is always measured relative to something, just as kinetic energy is measured in a particular frame of reference. That being the case, I could always make $T=V$ by choosing the reference in a certain way - but it will not generally be true.
For example, I can set $T=0$ at the top of a tower, or at ground level. Both are valid - it's really up to me. Or I can say $T=0$ at infinite distance from the earth.
And when I observe a falling object, that object will appear to be decelerating relative to a frame of reference that is moving towards the earth faster than the object.
Instead, you can say that
$$T + V = \mathrm{constant}$$
Because as you lose potential energy, you gain kinetic energy (assuming those are the only two forms that energy can take in your system). If you add friction, it's of course possible that the sum $T+V$ will decrease as the system warms up (unless you define thermal energy as a form of either potential or kinetic energy, which you could...)
But no, $T=V$ is not in general true.
Best Answer
Neither. Information isn't energy and can't be measured using energy units. As you pointed out, information is related to entropy which is about degrees of freedom in a system.
In physics, information is usually measured in nats but bits are common too.