George Scott It doesn't matter the order you read them. They are unrelated IMHO. Only one character is shared in the stories, and he has a small role in one of them.
Scribal I read Ship Breaker first but it doesn't matter. They are two different stories in the same universe (with one character appearing in both.)
Paula Kraft You might also want to put Windup Girl on your list. They are all stand alones but set in the same future.
T. Peter It only matters if you like reading books chronologically as the author wrote them. But as Paula Kraft (below) suggests, you can become familiar with the world encompassed in both "Ship Breaker" and "Drowned Cities" by reading Bacigalupi's earlier stories. While "Windup Girl" is a good start, a better one is "Pump Six and other Stories."