If I use it as it is I don't see anything! If I don't use style="display:none" inside the divs, I see them both initially and I can hide/show each one depending on which link I press. But the thing is that I need both divs to be hidden in the first place, and when I click on ONE, to show TWO, when I click on TWO to hide ONE and show TWO etc. Each time 1 div should be visible, depending on which link we press. The other must disappear.
Your example is setting both the "display" property and the "visibility" property. You have inline code that sets display:none, which will totally remove the item as if it didn't exist, whereas visibility will leave an empty box in the space where the item is located.
Depending on which behavior is the desired behavior, use only display or only visibility, but not both.