[mirimir]

The "outer space" boundary above any point on the surface does occur at the same pressure. And that boundary will also be an oblate spheroid. However, it won't have the same shape as the surface, given mantle inhomogeneities. But I have no clue what the differences look like.

[vacri]

The moon doesn't orbit the poles, but orbits (roughly) the equator. 'Distance to space' is orthogonal to the earth's surface, wherever you are standing. 'Distance to the moon' is not - for someone at the poles, it will always be to their side, never above their head. At the poles, your direct line to the moon will always have to travel some way across the width of the earth.

In fact, if you want to get really pedantic, then roughly half the time, the person at the pole will be closer to the moon than the person at the equator, when the moon has orbited to the opposite side of the planet to our equatorial chum...

[LanceH]

Distance from the center of the Earth may have worked better than proximity to outer space.

[mirimir]

True. But probably hard to determine.