The magnetic field of the Moon is very weak in comparison to that of the Earth; the major difference is the Moon does not have a dipolar magnetic field currently (as would be generated by a geodynamo in its core), so that the magnetization present is varied (see picture) and its origin is almost entirely crustal in location; so it's difficult to compare as a percentage to Earth. But, one experiment discovered that lunar rocks formed 1 - 2.5 billion years ago were created in a field of about 5 microtesla (μT), compared to present day Earth's 50 μT. During the Apollo program several magnetic field strength readings were taken with readings ranging from a low of 6γ (6nT) at the Apollo 15 site to a maximum of 313γ (0.31μT) at the Apollo 16 site, note these readings were recorded in gammas(γ) a now outdated unit of magnetic flux density equivalent to 1nT.
One hypothesis holds that the crustal magnetizations were acquired early in lunar history when a geodynamo was still operating. An analysis of magnetized Moon rocks brought to Earth by Apollo astronauts showed that the Moon must have had a strong (above 110 μT) magnetic field at least 4.25 billion years ago, which then fell to 20 μT level in the 3.6 - 3.1 billion years BP period. The small size of the lunar core, however, is a potential obstacle to promoting that hypothesis to the status of theory. However, single silicate grains with magnetic inclusions from Apollo rocks formed at 3.9, 3.6, 3.3, and 3.2 billion years ago have been shown to be capable of recording strong magnetic fields but do not. This supports the alternative hypothesis that the Moon never had a long-lasting core dynamo, consistent with the lack of energy needed to sustain a field.