I also have an MS in structural, but have many years working as an RE and in design with underground utilities and roadways. My feeling when I took the construction PM exam was that it encompassed many portions of the other depth sections. For example, as an RE you need to know how to troubleshoot if the soil borings from design are inaccurate, shoot grade, adjust grades that make sense (always seems like there's blown grades somewhere), change traffic control if necessary or required, adjust concrete mixes or HMA (in some cases), know the critical path from the contractor's schedule so you know when they are ahead of or behind schedule, understand cost take off if pay item quantities need to be adjusted, redesign in the field if the designer made mistakes or conditions are different, check designs if the contractor has a performance based pay item etc... There were "field" specific questions, but I felt that everything was pretty close to what I dealt with as a consultant. This exam is more of applying concepts from each of the other depths to a job-site.
I also see many engineers on here that work for contractors or are contractors. My personal thought is that design mixed with field experience bolsters your own resume and will only help you prepare for the construction depth. I don't have any experience in vertical structures or new development/real estate, so I don't know how that industry works (I'm in municipal and transportation/bridge work). Typically in transportation the RE is not a contractor, so my thought is many people miss out on this side of engineering, which I believe is invaluable experience. It seems like that might be why people miss the mark on the construction exam: either they have a lot of experience as a contractor, for example they know a lot about the PM side i.e. scheduling, cost take off, job efficiency which makes sense to me after working with contractors of all sizes or they don't have enough experience on a job-site in which case they have a wide range of design experience, but don't identify in one of the other depths. Just my opinion after reading through some of the replies here, on this thread and in past threads, and why people assume the test might be easier than the other modules.