I've had a loud trainer but she can be really quiet when needed with a more skittish animal. Honestly, I think she has and produces better horses than the quiet trainer I work with. She is very boisterous with an animal who is confident in her presence (or misbehaving) but is wise enough to tone it down when she first gets a horse or has a scared one. Heck, with my mare she screams shouts and cusses up one line and down the other and my girl throws her a dirty look. My gelding comes up for training and she's as quiet as a mouse with him. Her riding is very subtle and almost invisible cues believe it or not.
I don't think 'loud' or 'quiet' makes a better or worse trainer. I think it's the trainers actions that make a good horse. I've seen quiet trainers who beat the holy crap out of their horses and terrify them more than the loud ones. I worked with a quiet trainer once who was just like you described; his horses were scared to death of him. My trainer her horses adore her. I also think it has a lot to do with body language. For example: I can yell at my mare to stop doing something and she just looks at me, I can do the same with my gelding and he gives me the same look. My body posture throughout this is very non threatening despite my voice being loud. So I like the mix between trainers, sometimes horses need a loud reminder and sometimes they need a quiet one but a good trainer is one who can use them at the right time and place for the horse.
It's become a joke between trainers around here that we're some of the loudest trainers around because we'll be standing in a roundpen and see the horse go to unlock the gate and scream like we're being killed.
The horses just eat their hay and enjoy the show.