We are capable of colonizing both. However Luna would be the first choice. Why? If one were to colonize Mars first, it would be tedious to arrange the journey. You'd need enough food supplies to last for a few months for the journey from Earth to Mars, as well as people patient enough for said journey, and also enough for the return. Then you'd have to start stocking up for the demands needed by those who are colonized already. You'd also need to prepare on how to deal with the space effects such as degrading bones, going to the toilet, even drinking liquids because of the Zero-G environment. While the drinks and toilets (Albeit not comfortable) can be quickly dealt with, there is nothing to nulify the effects of bone degration. Hell, how would gravity control be managed in a colonized ship? You'd need to be able to find a way for people to walk around without helplessly floating about. Magnetizing the ship itself or wearing magnetized boots would solve the problem though. And that's only for the journey. Dealing with Mars' atmosphere is a whole different thing altogether. An effective biological zone would need to be set up beforehand to help deal with the mostly carbon atmosphere. At that initial stage only a select few would be able to be allowed to descend down onto the planet to help develop it's atmosphere, discover sources of water, filter them, set up a biosphere etc. Hell people could be waiting decades on the colonizing ship as it would effectively be a mobile living area, and supplies would be needed to be sent to the ship, including upgrades, power, food, workforce, etc. It would be a huge undertaking and would cost huge amounts of billions. Luna can be seen as a more scientific post for those out of orbit. The benefits Luna could pose to the science community because of it's cycle could be as simple as discovering how it really effects the earth, and also because of it's rotation it could be used as a launch post for other space journeys. Colonizing the dark side would be even more effective as it's directly launching away from Earth afterwards. The short distance also means that the journeys would be shorter. The fact that a low population (Maybe a few million perhaps) would cost less to handle due to delivery times, etc. While Luna has effectively no atmosphere to breath in, this would mean that the planet would be a strictly "Inside-Building" approach. Building underground could also lead to discovery of ore veins, seeing as the basalt make-up of Luna's craters are iron rich, could lead to a trading industry for industrial purposes. There would however, need to be a constant oxygen source for the inhabitants, so that would mean you'd need transport methods for huge quantities of water or ice that can be easily evaporated into breathable air without dissipating off the moon- which is why the strictly inside-building methods would be necessary. The costs would also be far less than it would compared to a colonizing attempt at Mars, and could also act as a try-test beforehand.