I almost always prefer adding stuff to a page with a constrained, fixed width. Of course the width will adjust to the device viewing the page, but building a page in a web app that uses the full width of the browser often ends up being ugly.
There's just too much space.
Contextual help messages will never span the entire width of the screen. If they do break onto a new line, the second line might be just a couple of words. Form elements gets too wide, and difficult to scan. Buttons can hide at the bottom, way out to the right.
Images rarely make sense in the full width of a large screen.
I'm writing this in Ghost, which splits the screen in half and shows markdown on one side and the rendered preview on the other. On a 30" monitor, even half of it is almost too wide.
But of course, some things do make sense to span across the entire screen. Even large ones.
Something like log files can often grow to extreme lengths, and the first 30-50 characters is often meta data that you want to scan down line by line without log messages breaking onto new lines.
Analytics reports can also make sense of the full width when done right - large charts or tables of data is not a bad thing at all.