The parallax Moon is considered to be a more exacting value of the Moons position because it is the average value between two points of observation on the Earth, taken at the same moment in time; if the distance between two locations is known and the angle of observation measured, the distance can be measured using trigonometry.
The parallax method is often used for finding the distances of stars, by observing the selected star from two different opposite points in the Earths orbit.
For the Moon
it is important that the observers can see the Moon at exactly the same time from different positions on the Earth's surface, then it should be possible to see parallax.
The distance from the Earth to the Moon is approximately 400,000km (250,000 miles). The Earth's diameter is approximately 12,756km (7,926 miles). This would be the maximum distance possible between Observer 1 and Observer 2. In practice, geographical (and meteorological!) effects will mean that observers are separated by less than the possible maximum distance.
By using two co-ordinates and the known distances involved, the exact degree location of the Moon can be identified.
Many astrologers including myself like to work with the parallax moon, because of its accuracy.