I have a couple of different polyfoam case types. I have a couple of Gator Lightweight cases. They are nylon on the outside, have a black velour/fur interior. Fit is great for my DV52, and they seem to have a rigid plastic backing sheet top and bottom. Closure is by zipper with a Velcro strap that does over the sipper pulls. Very suitable for around town, have a good compartment under the neck, and a nice sized outer pocket for music books or sheet music. Weak point is that the sides are cloth, so no support to speak of in the vertical plane. The shoulder strap hocks being plastic, will break in colder temperatures, but it does have a decent handle.
The second case is called the Forte case by Godin/Seagull/Simon and Patric/Norman (same case, offered by all the brands of Godin). It is an expanded polyrutethane case, with no cover (in my case, they do offer a zip up cover now in some models). The exterior is a dark gray. very dense. molded polyurethane foam with the handle being molded in. Interior is a flocked beige material It is heaver than the above Gator case. It is much more protective, both mechanically and in terms of humidity and temperature control. Snap closures, with a fairly good seal on the mating surfaces.The shell is rigid all around, so vertical plane impacts will be less of a problem than with the Gator. It has a decent inside pocket, but nothing on the outside. I think this could be used for a road case, as long as it wasn't packed as checked baggage (get a Calton on equivalent case for that). It is a pretty interesting design, you could stab it with a knife, and it probably wouldn't penetrate. Weakest point is the hinge which is a just a thin piece of plastic sheet and I have a concern about its longevity, but it hasn't failed in the ten years or so that I have had the case.
Both cases are significantly lighter than a full on, double arched wood case. I don't think the Double arched wood case is any more protective than the Forte case. The Forte case is also very good with temperature control (the expanded foam outer shell doesn't transfer heat or cold easily, and the mating surfaces are better sealed for heat and humidity than any wood case). The Gator is fine for moving a guitar around town with, but not for longer term storage at hot or cold temperatures.
P.S. You can get the Gator case to stay open by cutting the strap between the base a the lid. I don't even know why it is there, as the hinge on the Gator case is just a double layer of nylon fabric, so it's not like the hinge will be damaged, and I don't see how the strap would have anything to do with the alignment of the lid and the main part of the case. I may be remembering this wrong, but I think the zippers go far enough to the rear of the case to permit this.