I am a fan of full width layouts, or backdrops to be specific, but with boxed/wrapped content that has a maximum width.
Which you use is really up to you, or the clients, aesthetic tastes.
I cant think of any scenario where you would be forced to choose one or the other except perhaps needing more horizontal space to display something.
Or for mobile devices always full width with slight padding, because why take away screen real estate on small screens.
PS. I hate boxed header/navigation bars even if the content below is boxed. If you have a header bar of a different color it should be full width. But thats not a rule of the world, just my rule of thumb.