There's no reason both of those can't be done at the same time. The people/technology/equipment required to colonise Greenland or Antarctica have very small crossover with the people/tech/equipment required to colonise Mars.
(And while the money required is "the same money" - the costs of colonising Greenland disappear into the noise of the costs required to colonise Mars.)
Most of the tech is the same, only the transport differs. Getting people to live in a lava tube in Antartica permanently would at least tell us if the idea is feasible for the human psyche, it's basically the same as mars but warmer and with easier access to water.