Generally speaking, a higher brace height will quiet a bow with some minor reduction in performance. Because a higher brace height does slightly reduce the amount of power delivered to the arrow, it effectively slightly increases it's dynamic spine. Therefore, brace height adjustment can be used to fine tune arrow flight. Once you are tuned (straight arrow flight) left or right becomes a function of aiming.
I only adjust brace height to find a bow's sweet spot in terms of quietness and leave it there; then tune the arrow, arrow plate and nocking point for best straight flight.