The far more versatile choice is 「[地図]{ちず}」; No question about it. I would say that an average native speaker would learn to use 「マップ」 a good 10 years after learning to use 「ちず」 as a toddler.
In school, the word used is 「地図」 virtually 100% of the time and that is both in and outside of geography classes. In daily life, when you draw a simple map to show another person the direction to a place, that map is called 「地図」, but never ever「マップ」. Your collection of maps that you keep in your house or car are called 「地図」.
「マップ」 is most often, if not exclusively, used in proper nouns (as in 「グーグル・マップ」) and in naming little maps created for particular interests for inclusion in magazines, websites, etc. Those include maps of restaurants, maps of clothing stores, etc. in a relatively limited area.
Even when a map is named 「~~マップ」 in a magazine or website, you can still call it a 「地図」 if you want to, but the reverse does not work. You would sound pretty weird if you calledused 「マップ」 to refer to a map that has been named 「~~地図」 like 「[世界]{せかい}地図」 or 「[東京都]{とうきょうと}地図」.