For two observers at antipodal locations, the function MoonPosition returns contradictory altitude values.

The altitude of a celestial object as seen by an observer at North pole is the negation of the altitude as seen by an observer at South pole. Since both observers share the same horizon circle. Altitude 10° when seen from North pole is -10° when seen from South pole.

Moreover, since the shared horizon coincides with the equator, the declination of the object is the same as the altitude seen from North.

But altitude values returned by MoonPosition are different (altitude/declination is the last element):

northPole = GeoPosition@{90, 0};
southPole = GeoPosition@{-90, 0};
timeOfObservation =DateObject[{2016, 02, 28, 18, 0, 0}, TimeZone -> 0];

MoonPosition[northPole, timeOfObservation]
{23.93 \[Degree], -13.10 \[Degree]}  

MoonPosition[southPole, timeOfObservation]
{156.07 \[Degree], 11.34 \[Degree]}

MoonPosition[northPole, timeOfObservation,  CelestialSystem -> "Equatorial"]
{14.909 (()^(h)), -12.224 \[Degree]}

However, the function SunPosition is OK in this respect:

SunPosition[northPole, timeOfObservation]
{266.43 \[Degree], -7.98 \[Degree]}

SunPosition[southPole, timeOfObservation]
{273.57 \[Degree], 7.98 \[Degree]}

SunPosition[northPole, timeOfObservation, CelestialSystem -> "Equatorial"]
{22.743 (()^(h)), -7.976 \[Degree]}