Not relative to trailers, but it seems the box frames are being used more and more on HD pickups. The 2011 GM's are box, right? And Dodge for the past several years. Do you think this is because the boxes can be made lighter weight, cheaper or maybe both? The box frames seem to sometimes complicate installation of hitches and other accessories. I think I may have read on another web forum that the early B&W hitches for the 2011 GM's have had some structural issues.
You get the most bend strength out of a beam with most of its meat on the outer sides: like a C channel or I beam with heavy upper and lower flanges, and a thin vertical flange: bend force consists of compression in the upper flange and tension in the lower flange: the center doesnt do a thing actually. its called the neutral line.
However, a truck chassis as described above, might be very capable of carrying static loads, but it twists all over the place when under the dynamic, alternating loads on a road chassis: To get a more rigid frame with better handling, less body roll, less sway, etcetera, tubes are used because they handle torsion a lot better: the torsional resistance of a beam consists of the bend resistance over the X axis and the bend resistance over the Y axis: The I and C beams have very low lateral bend resistance because again, all the meat is in the middle, where it does nothing.
In Europe, Iveco (a Fiat division, made in Spain, historically notorious for their rust) claims that their C channel frames are less prone to rust. Mercedes (famous for their German anti rust treatment) uses a box frame, rust isnt an issue, and they have the most comfortable undercarriage which handles like a car, because of the overall rigidity, less body roll, less sway.
The difference in trailer building is that standardised, off-the-mill C and I channels are about 1.20 euro per kg: square tubing hits 3 euro per kg.
Especially in lighter trailers, the wall thickness of the I or C beam flanges are so thin that they flabber all over the place: thats why i build them out of trussed tubes. It sways less.