I was going to just write a quick answer, but I am long-winded and you’re getting a mini-treatise instead.
When I first planned my orchard, I was careful to select only those pear varieties with a reputation for FB resistance because I also have fireblight in North Georgia — bad enough that I had to finally remove my apple trees. I read over some academic literature and it seems that Shinko gets top marks for FB resistance, but the others I have planted also have a good reputation.
For Asian pears, I have Shinko, 2 x Korean Giant, Raja (newly planted and only on its second season), and the hybrids Daisui Li and Shin Li. The Shinko and Korean Giants are on callery, and the hybrids are on OHxF-87. The Raja is on BET (which is a bit of a gamble due to its higher FB susceptibility).
Precocity
Shinko was the first to bear, and now bears heavily every year. I got only a couple Korean Giants last year, but this year, both trees are loaded with developing fruit. Daisui Li and Shin Li flowered for the first time this year and set a handful of fruit apiece. If the trend holds, I’ll have more pears than I’ll know what to do with in another year or so. Notably, my Raja produced flowers on only its second season in the ground, but I plucked them in order to induce more vegetative growth this season.
Taste
I have only really personally tried (1) Asian pears from the grocery store, including named cultivars like Chojuro, and (2) fruit from my Shinko tree. (My family members sniped all of the Korean Giants last year and said they were very good, but I can’t personally do a pear-to-pear comparison.) It is worth noting that Shinko gets quite a few negative reports from growers in other regions, with some describing it as being bland, but that has not been my experience. The ones off my tree are quite sweet, with excellent crunchy texture, and are very juicy:
My Shinko fruit does not have the “butterscotch” flavor that some varieties (like Chojuro) tend to develop, but it is crisp and refreshing, and is at least as good as any Asian pear that I’ve ever gotten from a store. (Of course, this might be due to the fact that homegrown fruit is usually just better.) The fruit is good even if it is picked a week before ripening.
I am particularly excited to try Daisui Li this year. I remember that @castanea gave it very high marks in a post long ago, and so far in my fruit-growing venture (which includes jujubes and chestnuts), @castanea’s taste preferences have reliably predicted my own.
I have heard lots of great things about Drippin’ Honey — many people like @clarkinks who are in a position to know say that it either is outright the best-tasting Asian pear or in a small group at the top — but it is probably more susceptible to fireblight than the ones that I already have, and this deters me. As much as I would like to grow Drippin’ Honey, I have a good thing going right now and don’t want to risk adding in a potential FB reservoir to the club.
Flowering time
This year, all of my Asian pears flowered during the same week in about mid-March, with Shinko being the tail-end Charlie. As a result, I don’t think there would be pollination problems with any of these varieties at least when grown in the South (but I also have some European pears like Warren that bloomed around the same time, so I can’t say for sure who is pollenizing whom).
Disease / pests
From what I’ve read, Shinko probably has the best resistance to fireblight of all Asian pear cultivars, but the others I have selected were all chosen on the basis of their reputation for being highly resistant.
So far, none of my Asian pears have been afflicted with any disease — not even a single fireblight strike. This is remarkable because I know for certain that there is an aggressive fireblight strain in the area, and several of my pears are planted near to where some mature apple trees had to be removed due to repeated massive fireblight infections. Conditions should have been good for fireblight this year: a very wet spring with mild temperatures and all of the pears in bloom, but they were all either spared by chance or managed to resist infection.
Plum curculios have made an appearance, but for now, they seem to prefer my European pears. More concerningly, I have definitely observed brown marmorated stink bugs, but for now, their numbers are few (this could change in a single season, though). Since the wasp that parasitizes them (Trissolcus japonicus) has not yet made its way to Georgia, I may eventually have to start spraying the Asian pears with Surround to hold them off, but so far, I have not had to spray for anything.
Other than that, the only other pest of note has been aphids, which tend to attack the tender new growth in the spring. So long as they are not protected by ants, the natural predators (ladybugs and the like) arrive and make short work of them about a week after the aphid population booms, and no intervention is required. When ants are present to defend the aphids, dealing with the ants is sufficient to solve the problem.
Overall, I am very pleased with how productive and low maintenance the Asian pears have been. (On the other hand, I am still new at all this, and I remember thinking the same thing about my kaki persimmons until KSDS killed half of them over just two seasons; pride goeth before a fall.) The biggest work involved so for has not been spraying for diseases or pests, but dutifully spreading / tying down branches in order to develop good scaffold limbs — a chore that will hopefully no longer be necessary in a few years.
Rootstock / vigor
This is a little controversial to say these days, but I think callery is probably the best rootstock for Asian pears in the South. It’s true that callery are invasive, and everywhere, but there’s no putting the genie back in the bottle, and I guess there’s a reason they are so successful at colonizing this habitat. They have zero problem with the heavy clay soil, and handle both drought and soggy conditions very well. My Asians on callery are more vigorous than the ones on OHxF 87 and recovered from deer attacks better, and the ones on callery all came into production sooner. And last year, when we had an unusually hot and dry summer with several straight weeks of hot sun and no rain, the trees on OHxF started looking sad and shedding leaves, while the ones on callery remained pretty much fine.
Also, the rabbits are much fonder of OHxF bark – they almost destroyed my Shin Li before I protected it – and don’t seem to appreciate the flavor of callery, usually leaving it alone after taking out a strip.
I am experimenting with BET on my Raja tree, and it looks to be every bit as tough and vigorous as callery if not even more so, but sooner or later I am sure I will have to deal with fireblight, and my understanding is that BET is more susceptible. I would hate to lose a tree just because I overlooked a fireblight-infected sucker one week.
Appearance
The Asian pears are all attractive trees, and in my opinion, look a little more ornamental than European pear trees. My Shinko is notable for having particularly dark green leaves and for apparently having a more naturally spreading growth habit. Another standout for attractiveness is Daisui Li, which develops rather large leaves that are red when they first unfurl and makes the tree look striking when it is in bloom and covered with white flowers and young red leaves:
The other hybrid, Shin Li, also has large leaves that are initially reddish, but they aren’t quite as impressive.
Recommendations
I am a little biased by my own experience, but if I had to pick two Asian pears for growing in the South, one of them would be Shinko. Top marks for disease resistance, a particularly attractive tree, precocious, productive, and as far as I’m concerned, the fruit is quite good when grown in this region.
The conservative choice for the second would be Korean Giant — it also has a good reputation for disease resistance, and although I haven’t tasted a homegrown one myself yet, the fruit gets top marks for quality from most people online, and my family members who purloined my fruit last year endorsed it. If it is indeed better than Shinko, as I expect, I’ll be happy. Also, Korean Giant and Shinko seem to be advertised in a lot of places as being good pollination partners, so there would be less risk on that front.