Bear in mind, you are asking about a species, not a clone, so impressions about quality could vary quite a bit. I suspect that the ones from Fairchild are seedlings so probably best if you can get advice from someone who has fruited trees from their same seed source. If you think about it, what kind of responses would you get if you asked if asked questions about Mangifera indica, not specific clones?
It has probably been 2 or 3 years since I have had kuini. The ones I tried did not seem to have objectionable fiber. They are highly fragrant (some call them durian mango but the smell is nothing like durian, just very strong). I think the fragrance is supposedly linked a good deal to the skin. I cut up the ones we had & put them in the frig to minimize the odor. My wife liked them & did not comment on the odor when eating them but always asked when she opened the frig, "what is that smell"? The flavor was not exactly the same as mango but, if you had to compare it to something, mango certainly comes to mind.
I believe that kuini is a bit more tropical than mango so it may be more inconsistent there -- better for someone else to comment on that. I have been trying to train mine to stay compact (~12' height limit) but it is too early to say if that will be successful. I am skeptical that they would do well as a potted plant. They are supposed to be very resistant to anthracnose. I have heard that they are self-fruitful but I don't know for sure.
One thing you will notice with kuini (& also some other Mangifera species) -- new growth is a beautiful blood red color, very showy.
John