The benefit of the solid one piece is that is is usually the most watertight of the bunch, since water rolls completely off the cover, which hangs over the bed. The only real water entry points are near the front of the bed corners, (near the truck’s rear glass window), and of course, the tailgate area of the truck, which has a gap between the tailgate and the truck bed (and has nothing to do with the cover) that allows water to enter the bed.
It is important to note that there are two types of one piece covers, the ABS plastic type and the fiberglass painted type. A benefit of the solid one piece ABS plastic cover (ala Undercover) is their ability to be removed easily (in about 5 minutes) and re-installed easily as well (also 5 minutes). The bracketry stays on your truck and has minimal impact of the functionality of your bed when your cover is off the truck. The permanent-mounted painted fiberglass versions are typically not easily removable, with a few exceptions (like the Snugtop F2) and are typically only available at truck accessory shops that are dealers for those brands.
The drawback of the solid ABS one piece is that, if you ever need to remove the cover, you cannot retract or remove it on the spot like you can with the folding or rolltop covers. You must plan ahead and take the cover off at home or someone where you can store the cover while you utilize your truck without the cover. As for the fiberglass Tonneau, the biggest drawback lies in the difficulty of removing it and reinstalling it if necessary.
There aren’t too many manufacturers for the solid one piece, and Undercover owns most of the market for that type. As mentioned before, these are made of composite ABS plastic & polymers, and are constructed to prevent warping from direct sunlight.
Undercover offers 3 different models, the Classic, SE, and Elite, but also offers painted-to-match versions for the SE (called the LUX) and Elite (called the Elite LX) versions of those models. There may be some other brands out there, but Undercover is the best solid one piece ABS plastic tonneau brand we’ve seen.