The difference between the 2 is subtle but in this case, just as in English, similar :
Tous les jours is "every day," and chaque jour is "each day."
In this case, just as Cherry said, since the autor is using "toutes les" in the second part of the sentence, it would be more consistent to use "tous les" in the first part as well.
So: Vous allez chez le coiffeur tous les mois? - Non, toutes les deux semaines.