My favorite cases are those generic looking zippered canvas-covered polystyrene cases - real lightweight, physically protective enough for most purposes, and they offer more thermal protection for your instrument than the multi-plywood cases do.
If I need more physical protection, then I go for the Pro-Tec heavy duty cases. Same thermal protection as the polystyrene cases above, but the Pro_Tec's also have a thin plywood shell on the top and back in addition to the polystyrene core. Pro-Tec cases are failry heavy.
I use clay humidifiers and hygrometers in all my cases. I've noticed that I have to replenish the water in the humidifiers much more often in the plywood hardshell cases than I do with the polystyrene ones above.
Both the generic lightweight and the Pro-Tec cases also accommodate larger bodied ukes than many of the hardhsell ones do. Fremont cases, for example, only fit traditionally sized small-bodied ukes like Martin's or Kiwaya's. Also, plywood hardshell cases are not created equal! Fremont cases for example are realtively lightweight and use thinner plywood than DATT cases, for example. If you sit on a Fremont case, it will deflect and possbly harm your uke!!! An archtop case will typicaly use 5-py plywood and will not deflect if you sit on it. So not all plywood hardshells offer the same amount of physical protection. The strongest plywood cases are ones with an archtop.
I would have no hesitation in sitting on my ProTec polystyrene case. The combination of a light layer of plywood with the thick polystrene core make this a very strong case!
A friend of mine has an Ameritage plywood hardshell case that is real nice and very very expensive. It offers the utmost in physical protection because it uses a full suspension sytem (like you see in real high end violin cases) in which no part of the instrument is touching anything in direct contact with the outside of the case - these cases can get dropped from several stories high and your instrument won't be harmed. The Ameritage cases also have a real good built-in humidifying/dehumidifying system that is very cool if you actually use the system the way it is intended (i.e., it requires monitoring). But it doesn't do the thermal protection thing that the polystyrene cases do, and those Ameritage cases are HEAVY as heck!