The Persimmon cultivars I am trying are listed below. all are Asian Kaki with the exception of Early Golden which is a American. and Nikita's gift which is a hybrid of Asian X American. Of my own trees I have only tasted Fuyu, Saijo, and Tamopan. This is 3rd year planted for a couple of my trees, and 2nd year for most. I have tasted a few others.
The 2 most general categories of persimmon would be astringent and non-astringent. You can get into Pollination factors on astringency but I won't detail that here. Astringent's need to soften prior to eating, Non-astringent can be eaten hard or soft, and normally are best just as they start to soften.
The astringent ones you would most likely encounter in your stores would be Hachiya, or Tanenashi. Hachiya is very nice and grown commercially in California, but reportedly bears poorly in the southeast, and I have not planted it for that reason. Tanenashi was one of the earliest planted cultivars on the east coast and bears heavy and reliably, but most consider the fruit inferior and the ones I have tasted were comparatively dry and pasty. But I have never tasted one fresh ripened from the tree, so possibly it would be like comparing a tree ripened fig to store produce one.
Non-astringent you will find will most likely will be labeled Fuyu. Fig's are not the only fruit with naming confusion. Fuyu has at times been used generically for any non-astringent. Much of what is grown in California as Fuyu is actually Jiro, as well as some Matsumoto Wase Fuyu I have been told. I have Fuyu that have fruited from 2 different sources and they are different, but I have not had that many fruit to compare them side by side yet. I think most taste pretty similar and the degree of ripeness and when are they are picked is probably a bigger factor. You can eat a non-astringent any time after it colors ups, but I find them bland early compared to just before they soften.
Of Astringents I always hear positives on Saijo and Giombo.
Of Non-astringents I think all the Fuyu and Jiro and it's sports are pretty similar tasting, at least to my palate, which may not be that discerning. I know that Izu took 1st place at one taste testing that was done at the same time as a Pomegranate testing, but as Izu is one of earliest ripening NONs maybe the timing of the event factored in.
There are PVNA cultivars that are astringent when hard when not pollinated, but when seeded are supposed to be very rich tasting. I have tried a couple fruit, but have been trying to keep my fruit seedless, so those currently are not my focus. A couple of them would be Nishimura wase and Chocolate. I think more that one cultivar is sold as Chocolate as well. The flesh of PVNA around the seeds turns brownish as well related to the astringency leaving when seeded.
What I have to this point:
In Ground:Newly purchased planting soon:
Matsumoto Wase Fuyu
Newly Grafted on very small rootstock and praying:
Giomba (same as Giombo??)