At 2011-13 era, the E-series cutaway chassis had ratings from Ford as follows:
E-350 with 5.4 V-8, 13,000 GCWR, 7,700 maximum loaded trailer weight
E-350 with 6.8 V-10, 18,500 GCWR, 10,000 maximum loaded trailer weight
E-450 with 5.4 V-8 (rare), 14,050 GCWR, 8,500 maximum loaded trailer weight
E-450 with 6.8 V-10, 22,000 GCWR, 10,000 maximum loaded trailer weight
Prior model years (they've been making the E-450 at least 13 years, the E-350 cutaway more than 30 years) could have lower ratings.
These are for the cab chassis. You put something on the chassis, that takes away some of the GCWR for carrying the load, reduces what is left for the "tow rating." What you can pull, with a 10,000 pound hitch on the original Ford frame, is GCWR - actual loaded weight. This is where you are at when you rent an E-450 V-10 box truck from U-Haul, Ryder et al.
RVs are different. They are almost always extended 6 to 12 feet beyond the end of the OEM frame, and few RV manufacturers install a 10,000 pound hitch receiver. While the RV manufacturer usually does not lower the GCWR from the OEM specifications, the finished RV will often be given a "tow rating" much lower than Ford's "maximum loaded trailer weight."
The usual numbers are 5000 pounds for a flat tow, 3500 for a load on the hitch, with 350 pounds maximum tongue weight. Since Cruise America doesn't allow towing with rentals, most likely the towing equipment is install by them prior to sale, and only Cruise America knows just what the rating is. It will be not as high as U-Haul's ratings.
GCWRs and tow ratings don't have as much to do with engine sizes and power outputs as they have to do with the ability of the chassis to control the tow, gearing, and cooling capacities for engine and transmission. Distance from rear axle to hitch, length and strength of frame, are factors that change when you build a house beyond the end of the frame, not just put on a box that fits.