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One thing that makes answering this a bit tricky is determining how to measure. The Moon has no "sea level", so the comparison that makes the most sense is to measure from the highest point to the lowest. On the Moon, this is a bit over 18km. On Earth, Mt. Everest is at nearly 9km above sea level, and the deepest point is the Mariana Trench at not quite 11km below sea level, for a total difference of well over 19km.

By that standard, the Earth's mountains are taller than the Moon's mountains. However, the difference is only about 10%, and the Earth is a lot more than 10% bigger than the Moon, so proportionally speaking the Moon's mountains are taller.

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