My answer reflects my observations, and not of any written edict saying that things are done "this way" or "that way".
Except for forms, CDK and ITF can be very similar. Except for ultra-conservative ITF (who perform their techniques with a sine-wave motion), the methods of executing the techniques are very similar between them: stances are wide and low, and tend to do their forms so that there is a definite "pregnant" pause between each movement.
All styles of TKD generally have the same basic kicks. w*f doesn't use the butterfly (aka, inverse roundhouse - which looks like a front kick thrown to an outward angle). But this kick is a signature Tang Soo Do and Hwarang Do technique, and depending on your instructor's influences, it could be a staple in a CDK class too. I never learned it, but I see it used in breaking techniques in many TKD tournaments and tests. However, using this kick in w*f sparring or breaking WILL get you warnings or disqualifications, because in w*f, it is not a recognized kick. As has been explained to me, the kick is often used by inexperienced people attempting aborted front kicks. Therefore, it's sometimes hard to tell if the kicker meant to throw a front kick or a butterfly. w*f addresses this by not allowing the kick, except perhaps as creative elements to breaking routines.
w*f doesn't use the crescent at all except in forms. CDK and ITF, on the other hand, will use them much more. The reason is the crescent is best executed with a low center of gravity, whereas w*f's preference is to push the envelope as far as balance is concerned. So for w*f, the crescent is slow to them, and when done like their other kicks (high, fast, and just at the edge of balance), the kick is not effective for them.
As to the advanced kicks, you'll see a lot of flashy jump/twist/flip kicks in w*f than the other styles - even in sparring (ok, maybe not flip kicks...) CDK is a more conservative style, like ITF, and prefers to keeps the kicks at head height (or less) without a jump. Schools versed in Taekkyon, or w*f, or even Chinese style influences will often do these flashy jumps as part of demonstrations or whatnot. But for the most part, CDK prefers the kicks that are safer executed from the ground, or jumping with a lower target.
As to punches, w*f is fanatic about chambering at the hips, while ITF prefers the chest. I don't know where CDK falls on this issue. I recall my early years chambering at the chest, but I also recall recently CDK students chambering at the hip.
If you go to a CDK school, expect the manner, behavior, and ideology to be rigid and, at times, militaristic. For instance, many CDK schools will insist on recital of a membership oath famous for CDK schools, and also a few schools rules. They will salute the flag before entering or exiting the dojang, whereas non-sine-wave ITF and w*f (if w*f does it at all) will usually bow in and out. Attention stance is expected when speaking with a CDK senior. If you are spoken to, either be at attention or an "at-ease stance" (where hands are at your rear, overlapping and palms out, feet shoulder width apart).
w*f schools - ultra modern ones - tend to be less focused on militocracy. Respect is give-and-take, but it's not as rigid as CDK. I recently was part of a tournament planning session. It consisted of black belts from 1st to 6th degree. No one observed any sort of hierarchy, and the attitude was "get the f*cking job done, and don't p*ss off the grandmaster". Kind of funny, I though. But that seemed the theme of things at most of the w*f tournaments I've been at. You'll get respect with more stripes, but by and large, whoever has expereince (and not necessarily the stripes) gets to command.
CDK schools have a tendency to not give out black belts to children. ITF and w*f seem to give out BB to folks as young as 8 and 9 (I recently attended a tournament with 9 rings - 2 were dedicated to "7-9 year old black belts". This was a tournament that was hosted by a Hwarangdo school, with about 50?ttendance of ITF students, judging by the forms they performed. None were CDK.)
CDK itself is an organization that was once considered a separate style of taekwondo. But now, they are a fraternal organization (not sure what this means). But the more conservative CDK schools will issue their own dan certifications. Most of the modern ones are under the umbrella of Kukkiwon, and therefore, are supposed to be IDENTICAL to w*f. And that is hardly the case: they will perform Taeguek forms, but they will do them a la CDK traditional. Very few schools refer to themselves as CDK and then rigidly follow Kukkiwon.
I hope others can give you their experiences - I think Karate Dave has experience in CDK, so he might be able to give other perspective too. And Cheetah has ITF and w*f experience, too.
Answered By: possum - 11/19/2011