Moon colony is easier than mars colony, but not by much.

So it seems very obvious that going to the moon is much easier than to Mars. We did it already! Whereas no man has even set foot on Mars yet. And it is true, the Moon is much closer and it takes less time and fuel to get there. The journey to the Moon takes ~3 days, whereas the journey to Mars takes months*.

So that's it right? Well, not quite. Getting there easily isn't everything, you also want to stay there and build a base/colony. And this is where Mars does have some key advantages.

• Gravity. We know that zero gravity environments are harmful to the human body, degrading our bones, muscles, and causing issues with our bloodflow and immune systems. What we don't know is how the long-term effects of low instead of zero gravity looks like, but it stands to reason that the closer to earth gravity we are, the less severe the effects will be. The moon has 16.5% earths gravity, Mars has 38%.
• Atmosphere. The moon doesn't have one, Mars does. Why is that important? Radiation. Space is full of it, and the sparse Mars atmosphere blocks at least some of it. To be honest though, this doesn't seem to be a big difference, and either way whats likely to be more important is how good our radiation protection is.
• Dust. Because Mars has a bit of an atmosphere and winds, there is abrasion, so martian dust loses its edges over time. Not so on the moon. Dust on the moon is highly abrasive due to its jagged edges, and on top of that electrically charged, making it much harder to remove. This article puts it quite nicely, the apollo missions were on the brink of failing after just a few days on the lunar surface.

Fuel economy also isn't even that much better, if you look at hohman transfers, the moon takes 13,7 km/s to get there, whereas Mars takes 15,1 km/s.

The only reason why the Moon is safer is because if something goes wrong, you are out of there quicker when something goes wrong, and you can get supplies there faster if something breaks. For Mars, once you're there, you're on your own for a long while, so you really have to be very certain that nothing will go wrong. Basically, the moon is a test bed. In that way, it might actually be good that it has harsher conditions than Mars, so we can be more confident that if it worked on the moon, it probably will work on Mars too. But if you really plan to stay there for a long time anyways, Mars should be more accommodating.

\Depending on when you go 6 to 9 months… potentially less if you burn extra fuel that you might be able to spend due to Starship refueling? So some claim 3 months. Regardless, a rather long time compared to the moon.*