This question is similar to my other question "would walkers work on airless worlds?", however even though it's the same setting and I am talking about the same battle group tactic that question dealt with the big boys of war, the vehicles so big it would scare a "Deserts Of Karakh" tank Commander (I don't know the exact size of the things), this question is about vehicles on the size order of an m1 Abrams or AT-RT (two legged walker about half the size of an AT-ST), the main purpose of these is as anti-infantry or ant-anti-Walker vehicles. So a far different discussion.
So for a bit of background on the scenario: the earth-moon system is engulfed in the greatest war it has ever seen, a war waged between powers on both worlds over the fate of the earth-moon system. That's all I have so far... I am talking about fighting on the moon in this case but it applies to any space-rock without an atmosphere.
Since I am trying to figure out the small boys I am simply trying to figure out which is better, tanks or small walkers. They're mostly anti-infantry or anti-vehicle so they require the ability to carry either weapon and to be fairly quick. I am currently for small walkers so let me list of the reasons why.
Now the tanks have the advantage that when tread is blown it doesn't normally crash, two-legged walkers do, four-legged ones similar to crab droids would become stationary. But Walkers have one huge advantage, the lunar dust! if you don't know the lunar dust is so fine that it will get into electronics if it gets stirred, the problem is so bad that any wheeled vehicle would likely stir up so much dust that it could explode because of the amount of dust in it, consider multiplying the amount of deadly dust stirred up by a tank and multiply that by the amount of dust hundreds of tanks would stir and you have the big problem of more than half of them blowing up on the way to battle, consider now how reduced the problem is when you walk on legs, and fairly high. A transport walker (like the AT-OT) could fix the problem of the en-route problem but the dust could still destroy many tanks during the battle.
Edit: Credit to TCAT117 for convincing me that in the case of small vehicles tanks are better, even on the moon. my main concern was that the lunar dust would be a big problem, but it wasn't, and that low g would force the tanks to go ridiculously slow, but war is slow. The jury's still out on number two, I'm keeping this on still because if a pro-walker person can prove to me that walkers can easily go faster than tanks the small walkers will be more important than I am currently going to make them. I'm still going to have big ones though.
Edit: I have come up with a bit more on the scenario that should give you a better idea about why these ground forces exist. First of the earth and moon are both separated between many different governments: the earth is split between a few dozen to over 300 separate nations, the moon probably has over 2,000 nations (the exact number isn't important). but the Lunar armies are for this nation on nation combat. If your attacking from earth the combat will be different.
So far so good, I am getting alot of answers talking about the uselessness of land vehicles on the moon and if you think you have something to add then please address it, all of the discussion around that however was before the edit above so I would ask that anyone with that viewpoint fit their answers to the more detailed addition to the scenario on edit two.
But if you want to discuss the how different land vehicles compare then it might be helpful to know that the main factor I am considering is the Lunar regoliths ability to destroy vehicles in transit.