These questions cover an immense amount of ground in terms of knife design, knife technique and their interrelation.
Let's start with the last. At the risk of being obvious, the "right" knife for a given task isn't always the best choice for a given user -- even for that task. And it gets fuzzier from there.
Now, the first. There are three principal types of Japanese design boning knife: honkotsu, honesuke, and garesuke. The popularity of the shapes depends somewhat on purpose and somewhat on region. Honesuke and garasuke have very triangular shapes as a result of their wide heels. They're used primarily for chicken and pork. The honkotsu is shaped most like a traditional European boning knife profiles (desosser and fillet), is most popular for boning beef, and is most popular around Hyogo and Osaka.
Before going further with the profiles, let's get some butchering terminology down as it applies to chicken. Breaking down means cutting into serving pieces. Breaking means splitting the back bone, keel bone, or any of the other main bones. Jointing means separating the pieces at the joint.
A garasuke is a heavier version of a honesuke -- and usually longer. Garasuke and honesuke are not meant for removing bone in the western way, but for cutting through it. The Japanese like to chop the knuckles off the bones, cut the breasts into pieces across the ribs, and all sorts of "chopping" cuts we don't use very much in the west. From a design standpoint these profiles are not particularly good choices for jointing chicken into the cuts we think of as normal (half-breasts, thighs, legs, wings, supremes, quarter-breasts, etc). Certainly though, you can make either work well if you've a mind to do so. They're also not great designs for taking the meat from the bone to make boneless thighs. For that you want a knife with a lot of radius right at the tip, so you can keep the handle up as you cut next to the bone. The best choice is probably a petty; second best, perhaps a European boning knife. (It really doesn't matter with a breast, the meat comes off so easily.) But again, if you keep your honesuke or garasuke sharp they'll do the work almost as well as anything else. Sharp always trumps.
The honkotsu's blade profile sort of falls between the slender desosser style Americans think of as "boning" knives, and the slightly wider filleting style. It's much heavier than either European knife, and has a much wider handle. If you're comfortable using a European style boning knife, have the technique, and so on, it will do the same things in pretty much the same way. The Japanese profile is maybe a bit more useful for "frenching" and a bit less for the kind of intricate work required to take a lamb leg and hip bone, out of a sirloin/leg. Hard to say.
Some European boning knives can be difficult to sharpen because they're made out of fairly thick stock and have a narrow profile without much grind. In other words, they're shipped thick at the edge. Most sharpeners, even (what passes for) professional sharpeners (these days), don't know how to sharpen a good edge on that kind of knife. (More about this later.) Honkotsus are made of even thicker stock, but there's so much grind on one side (very right-handed is standard) they're faily easy to sharpen the first few times as long as you've had some experience with asymmetric edges.
You also asked about flex in European knives. Generally, stiff is preferred for larger mammals, and flexible for fish, poultry and small mammals. Flex is more useful when the knife is pressed against the board, then anything else. Sharp kinves will cut through (or at least into) bone before bending enough to follow a complicated shape. Curved knives make it easier to do slicing and steaking without hitting your knuckles against the board. Straight knives are easier to control for intricate work.
I was trained to do light boucher work when I had a job at a big deal French restaurant called the Blue Fox in San Francisco in the early seventies. I use the same sort of knife now as then -- a medium flex, carbon steel, Sabatier desosser. The current knife is a Thiers-Issard Elephant Sabatier.
The best way to keep the European style knives sharp is to thin before sharpening. Sabatier carbon will hold a 15* edge against a lot of abuse, so I sharpen a 10* bevel, then a 15* edge over that (15*/10*) -- and a little more acute than that at the tip.
Too much polish is counter-productive in a knife that sees so much raw, red meat; so I usually stop at a soft Arkansas -- the equivalent of about 1500# JIS, although sometimes I take it all the way up to a surgical black Arkansas (about 4,500# JIS). 2500# JIS would be close to ideal. Once sharpened, the knife maintains fairly well on a steel.
Because they're so asymmetric, the Japanese profiles don't usually steel well. That's really unfortunate in a knife that bumps up the board and bone so often.
My feeling is that all in all the European styles are better suited for European style work, and that they maintain better as well. However, knife purchasing isn't necessarily about pure practicality; and even if it were different people like different things. There's no best, only most comfortable.
Hope this helps,