I haven't actually eaten much summer squash. Winter melon is sort of firm when raw, sort of mushy when cooked. It FEELS a lot firmer than raw zucchini does (somewhat tellingly, raw winter melon is sort of translucent not opaque like zucchini.)
It's only really potato like if you are in the habit of BOILING potatoes, and very waxy ones at that. It never really softens up into mush, but eventually I will end up crumbling into semi gritty stuff.
One of the reasons I say a boiled potato is that I can't think of any recipe using them where they are NOT boiled or steamed.
The standard form is as I said winter melon soup, or more accuractely, soups since there are at least two of them. The winter melon is really there for bulk and texture, not flavor (it really doesn't have much of one). The flavor comes from the chicken stock (actually since this is Chinese cooking it's some version of superior broth, which is MOSTLY chicken but also has some scallions, ginger and ham added) and what you add to it. As I said there are two main versions. The commoner is Eight Precious ingredients, where the melon is mixed with an assortment of things, usually ground pork, shrimp, peas, egg,mushrooms etc.) For banquets it is sometimes common to take a whole melon, cut the top off (like on a pumpkin if you are making a jack-o-lantern) scrape out the insides for the soup, carve the outside and use it as the soup's tureen. (they sometimes do the same thing for dessert soups, but there they use a watermelon)
The less often seen (because it is regional) and the version I personally prefer is Shanghai style. In that one all that is added besides the winter melon is more Chinese ham (Chinese ham is a country ham (like prosciutto) as opposed to a city ham (i.e. the pink boiled stuff used in sandwiches) but a LOT saltier. a drier less supply version of this is also often served as a summer picnic dish since winter melon is considered a "cooling" food.
The real problem is that neither soup uses all that much. When I go to the Chinese restaurant and get a quart of soup there are probably 4-6 oz. of winter melon in there. And a whole winter melon is indeed usually huge. Canton giants are usually somewhere in the 80-120 lb range when whole. Most of the other are a bit smaller, but 50+ pound fruits are pretty normal. It's one of the reasons I don't grow it, I'd end up throwing away 95% of each fruit to spoilage before I ever got around to using it. Though I saw the Kintazawa list at one point and I think a few of theirs are bred to make smaller more "family friendly" fruits of 2-5lbs (still a lot of soup but an amount a family of 4 could probably manage to get through.)
Without those it's probably a better idea to go for winter melons cousin, the hairy gourd (also a Benicasa) That's a little firmer (actually that gourd really IS like summer squash) and you have to peel it (unless you like coarse hairs in your throat) but the flavor is similar, and they tend to be more reasonable in size.
