Answer: It absolutely depends on the individual person, the emotion in the room, and what part of labor she's in. For the beginning of labor, the mother breathes through contractions and I breathe with her. My breathing guides hers. I help her control the speed of her breathing and how deep she is breathing, not by telling her she's doing it wrong, but just by modeling how to do it right.
If/when she begins to make noise, the principle remains the same. Deep, low, moaning sounds are productive toward birth. They are empowering. However, high-pitched screaming sounds are not productive toward birth. They are fear sounds, it usually means she is not on top of her contractions, they are on top of her, so to speak. By helping her control her pitch, I am helping her to keep fear and panic away. When I moan with her, I keep my sounds a touch lower and a touch more controlled than wherever she is at. It serves as a guide. Often, she will match me in pitch, as if I am the conductor. But at the same time, she is the one who is choosing the song, since she is the one who is in the experience.
The last reason for moaning and later roaring along with the mom is so that she doesn't feel so self conscious. Many women are afraid of losing control in labor, and afraid of the sounds they might make or that they will look or sound stupid to others around them. They don't want to "bother" others. They don't want to scare their partners or to be judged by people in the hall or lobby. You know how it is much easier to sing in front of a crowd of people if you are part of a group than if you are doing a solo? By making her sounds with her, I am essentially giving her permission to express herself and not feel like everyone's eyes are on her. Her birth is no longer a solo, it becomes a duet! Sometimes partners or nurses will even join in. Most moms love this!
I did hear a story about a woman who told her doula to shut it, but it hasn't happened to me yet. If a client told me that she would prefer a quiet birth, I would be happy to support her in maintaining her best birthing environment. But for the most part, these aren't the women who are making the roaring sounds in the first place. Everyone is different, so of course there are mothers out there that would get more out of the doula being quiet, even while they roar, but I just wanted to stress that loud and calm are not necessarily opposites. My presence is both.