Ive done abit of all 3 in the past so Id like to think that what Im about to say wont be complete waffle.
Tae kwon do is supposedly the most scientifically structured martial arts around today as it only came into existence in 1960 or so in Korea, I think, due to its waring history and the desire for its people to be able to defend themselves. Its pretty structured and all about using momentum while keeping the body pretty rigid to do extra damage. Like was said its a striking art so theres very little grappling or holds. Its more practically oriented then Karate though, with

of emphasis on sparing after certain grades have been reached.
Kickboxing is a real scrappers fighting method. Focuses

on physical fitness and patches movements and holds/grappling from all forms of other techniques. Very freeform sparing and EVERYONE does it, even if its your first day. Gets interesting when you get a few belts under you and they start sparing you against the blackbelts.
Karate then was long ago but I remember it being very structured, lotsa discipline and forms. Wadu ryu concentrates

on stick fighting as it was developed I think as the sword was being phased out.
Hmmm far as I can tell that does sound pretty convincing. Enjoy the bruises.