Mars is often disussed as a target for mass colonization and eventual terraforming, notably by SpaceX. The Moon does not seem to be viewed as a future 'alternative' to Earth in the same way that Mars is.

Stats to consider:

Distance

• Mars: between 55 and 400 million km from Earth (0.37 to 2.7 AU). It comes nearest to Earth every 2.14 years, or ~26 months.
• The Moon: ~0.38 million km from Earth (~0.0026 AU).

One-way communication lag

• Mars: between 3 to 22 minutes
• The Moon: ~1.3 seconds

Gravity

• Mars: 0.38 g
• The Moon: 0.17 g

Rotation period

• Mars: 25 hours
• The Moon: 1 month

Atmosphere

• Mars: mostly CO2, at ~1% the pressure of Earth's.
• The Moon: negligible if any.

Solar energy

• Mars: ~44% of Earth's, but occasional dust storms can bring this down to almost nothing.
• The Moon: same as Earth's, but with no clouds or other interference.

This question is resolved when either the Moon or Mars has 10,000 people living on the body who have been residents for 3+ years at the time of counting. I've chosen 3 years to exclude people who arrive on Mars during one Earth-Mars opposition and leave during the next.

Residents of Phobos and Deimos, or of satellites in orbit around either body, are not counted for this question.

'Residence' is defined and determined by the government or entity administering the colony, or a similar official source.

In case political structures are substantially different, an admin may judge this question based on a different definitions of 'residence' that still captures the idea that it requires a person to have lived there for at least a relatively uninterrupted three years. Ems don't count as humans.

Resolves ambiguous if neither body meets the criterion by 2100.