Which is more important, liberty or freedom, and why?
There are various ways of distinguishing between liberty and freedom. I will answer this question using the distinction discussed in the link below as it is the distinction with which I am most familiar. In my view, freedom is more important than liberty because our freedom protects our liberty and makes it possible.
According to this definition of the two words, freedom can be seen as the state of being free from control by an outside source. By contrast, liberty is more positive in that it grants you the right to do something in particular. For example, if you have the freedom of speech, it means that you are free from attempts by the government to prevent you from expressing yourself. On the other hand, if you have the liberty to say things that are offensive to other people, it means that you have the right to say those specific kinds of things. Freedom, then, is a negative thing in the sense that it is the absence of outside control over you. Liberty is a more positive thing in the sense that it is the affirmative right to do specific things.
Of course, both of these are very important things. However, I would argue that freedom is more important because we would not have liberties if we did not first have freedom. Our liberties are very important. They include our liberty to speak our minds in public and our liberty to worship as we wish. They include our liberty to disapprove of our government and to speak out against our leaders. These are things that we should and do value greatly.
However, it is our freedom that makes these liberties possible. We have freedom from excessive government control of our lives. This is the most important thing because it means that we live in a society where we can expect the government to leave us alone in many ways. Before we can exercise our liberty to say that President Obama is a socialist or that Donald Trump is a fascist, we need to have freedom. Before we can exercise our liberty to belong to our particular churches and worship in our particular ways, we need to have freedom. Freedom is the overarching condition of being free from control by an external power. We have to have this freedom before we can have our specific liberties. Therefore, freedom is the more important of these two things.