I may be rusty in my understanding of orbital mechanics, but here's a try:
At apoapsis, an orbiting object will be travelling at the slowest velocity of its orbit. Hence, if you make a plane change at this point, assuming you are not changing any other orbital parameters, the velocity at your target orbit will also be the slowest velocity along that orbit. All you're really doing is changing direction, and so that's going to be easier when you're moving more slowly, as opposed to periapsis, at which point the the orbiting object will be at the fastest velocity of its orbit.