The Moon gets bombarded by meteors at the same rate as the Earth according to
Does Mars or any other planet get bombarded at the same rate as the Earth and Moon?
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I recently wrote a paper that talked about some of this, so I have a fair bit of info on it.
The canonical number today is that Mars' proximity to the asteroid belt means that, for asteroids, the bolide ratio between Mars and our moon is 2.8, meaning that it gets hit 2.8 times for every 1 time the Moon does, per unit area. This is from a book chapter by Ivanov et al. (2002). The reason that we can approximate this based only on asteroids is that asteroids probably account for about 90% of all impactors in the inner solar system, and comets should be about equal between Moon and Mars.
Then, you scale by surface area since bolide rate is per unit area. Mars has roughly 3.8x the surface area as the Moon, so we would expect about 10 more impacts to form on Mars per unit time as on the Moon, in the current solar system configuration.
Where this becomes really kinda hairy is when you go back in time to maybe the first ~half-billion years or so. With lots of possible dynamic rearrangement going on and scattering of small bodies (what happens if Saturn and Jupiter move farther out in the solar system?) the impact populations were different, and the bolide ratio was also probably different. The fraction of comet impacts was higher, leftover planetesimals from planet formation was a population that you have to account for, etc.
And, the dynamical models to not agree. The best I can give you at the moment is that the bolide ratio was anywhere from about 1 to 5 early in the solar system (review by Bottke & Norman (2017) is reasonably understandable).
We can try to use the impact crater record (what I study) to try to at least constrain the problem, but the impact crater record on Mars has been partially obliterated, including the oldest stuff, so it is hard to use that as a constraint. That was the topic of my paper (Robbins, 2022) where I lay all this out and tried to write it at a level that a non-technical audience could get the gist of, if you're interested. This paper approaches the problem from the largest, oldest craters on Mars and the Moon and points out that if you assume today's dynamical models are correct in the ancient solar system, then Mars is missing ~40-80 craters >1000 km across. I then went through several different ways to reconcile the observation with the models, and I think the most likely explanation is that you really did need to have a very different bolide ratio in the ancient solar system than present-day.