Persimmon is an extraordinary wood in several ways. First is its hardness. As the only domestic wood in the ebony family, this is no surprise. No wonder it is the wood used in golf club heads. This means you need to be super sharp to work it with hand tools, but it is not as difficult to work as its hardness suggests. In fact, it melts away beautifully under a rasp in any direction, I suppose because it lacks any of the stringiness you find in oak, hickory or black locust. This lack of stringiness makes it an excellent carving wood (much like ebony is) because you can come at it from most any angle and it will leave an exact track of what your gouge has done. This may not always be a plus if your carving skill matches mine, but it is incentive to up your carving game.
Once it is shaped, it will take a very high polish, so sand it to the highest grit you own. It will shimmer like marble.
Contributing to the marble-like appearance is its coloration. The only jet black parts are inevitably near a check, so the usable wood is mostly a cream color with wisps of smoky grey streaking through it. I find this attractive on its own - like marble - but compared to the clear single color of a nice maple or gingko some might consider it "dirty" looking. Personal preference I suppose. Even more than the maple or gingko its lacks any prominent grain or annual rings.
Not that you will be making many loom shuttles, but this wood has high wear resistance, probably due to its high silica content. I am guessing this is another side of the high polish characteristic. In any case, if you have a situation calling for lots of rubbing, consider persimmon. I have used it for drawer sides and runners and I doubt they will wear in my lifetime.
Persimmon moves a lot when drying but I have noticed no particular issues once dry. As mentioned above, the black heartwood is a very small portion of a board and this part inevitably checks as it dries, so between warping and these checks, finding high grade boards can be a challenge. We do our best, but we end up with a number of smaller boards as a result. If you want to make a table top of persimmon, expect it to include character. This can be very effective. Take a look at the vanity one of our customers made from persimmon:
You can dress it up too. Here is a crotch piece with a blackwood accent:
We get a few persimmon logs and saw it 8/4 most of the time to assure we have something usable after it warps. The pieces are certainly larger than any ebony you might find, and at $5/bf, it is much cheaper.
I personally have very little experience with ebony. I am put off by its environmental reputation, so I am glad that my experiments with india ink and sanding to high grits are a very successful substitute:
I hope you can tell that I love persimmon. It is a favorite discovery in domestic hardwoods.