If you eat them too soon (and if you ate them off of the tree, you ate them too soon) they will make your mouth pucker for hours. Allowed to ripen fully, they are very sweet. I wait until they fall from the tree. Most years, this is around the time of first frost, but this year they started dropping a month early. Wen ripe, the native persimmon is very soft, with wrinkled skin, and flesh that is mushy, the consistency of purée.
Persimmons can make good wine. Scroll down a few threads for "Persimmon wine variations." In that thread you will see that Terroir is "thrilled" with his persimmon wine. You will also see that mine (I have done four batches totaling 9 gallons) get what to me is a funky smell around day three in the primary. Just today I racked my first batch again, and I'm happy to report that is is coming along very nicely! It makes what I would call an earthy wine which I imagine to pair with mushrooms, root vegetables, roasted foods, etc. So far, the versions of persimmon wine I like best are the batches I've balanced with some orange.