If you're a buyer, you love a quiet sale because with a quiet sale you don't need to compete. 

As a seller, you might choose a private sale if you'd prefer to sell your home to someone you know, or if you want the convenience of working with only one buyer. 

BUT, if your primary goal is to maximize your return on investment, then fully marketing your home and exposing it to the entire market is the clear choice. Here's why.