Choose a referee who knows me better or one who is better known? I'm currently choosing my second referee for a masters application. I did an academic internship and I worked closely with two people while there. One of the people was the Director of the institute and is more experienced than the other. However, I know the other person better and believe she would write a better reference. Should I go for the person who may be better known in the world of academia, or the person who will write a better letter?
On any sort of application, for school or a job you want to build a portfolio that highlights your suitability for the desired position. Neither of your referrers will be there with you if you get the position. All they can do is speak to your suitability as they see it. 

So, choose the one who can best speak to your abilities and general characteristics that suggest success. This would seem to suggest the "other" person. 

However, you know something about each of them and are a better judge. But it isn't the capabilities of those giving references that will be judged. It is what they say about yours. 

Later in your career it might be different, if you have a powerful sponsor who will continue a collaborative association with you going forward.