Both are valuable, and they reinforce each other.
Pieces already memorized
Since your hands and ears already know the feel and sound of the music, it makes it easier to associate the experience with what you're taking in visually. This also allows for the possibility of playing music that might otherwise be too difficult to read fluently.
"Reading" music you've already memorized helps develop the visual part of reading.
Brand new pieces
With brand new pieces it's important to start very, very simple. In general, learning visual cues is faster than associating those cues with physical or auditory experience. That is, recognizing by sight that two notes are a third apart is easier than developing the feeling of a third in one's hand or the sound in one's ear. This isn't true of everyone, and might not be true of you, but it's the most common situation.
Playing the simplest pieces lets you develop the association between what you see, what it sounds like, and how to move to play it without undo complexity. If one also have to contend with complex rhythms, intricate technique, or other musical factors, there's not enough room in one's mind to take everything in and play it at sight.
"Easy music", for me, means easy enough to play the entire at or near performance level after, at most, three readings. Reading 1 gives the basic idea of the music; Reading 2 allows for integrating the things noticed but not executed during Reading 1, and by Reading 3, "real" music is being produced (within the musical limits imposed by the simplicity of the music).
Brand new pieces develop the kinetic/tactile/auditory part of reading music.