The "Takoon style", is like Nicolass says - kites with good depower, and that can be flown very close to the window edge, with a profile that is not too cambered, to avoid losing control, when your speed increases.
The "opposite" kitestyle would be the North Rhino or the Gaastra GXR in these respects.
They have other advantages, especially in light winds.
The Wook is a middle AR (quite high AR in fact) performance kite.
Not suited for students very first kite attempts - as here a very low AR or two liner would be better, for relaunching.
It is very easy to fly the Wook, because it will not stall backwards - so you don't risk oversheeting.
With the Skoop you must be a good pilot, so you don't do this.
And for jumping - beginners or intermediates (or skilled - some prefer this style - kind'a wakestylish), you can just send the kite UP, or a little BACK, in a normal jump - and then don't worry about the kite from this moment, as it will just sit parked up there and lift good.
This is the reason why most people would be best suited with this type of kite.
Whereas the Skoop flies a little faster, and need speed to perform.
This means that in jumps you must control and fly the kite much more, to obtain the max. power from this type of kite.
So you must often learn to control the kite in the air, while you "do your stuff" in the jump - rotations/board offs/whatever...
This of course demands more from the rider, but you will be rewarded if you can do it.
The reason why the Skoop2 has such power jump takeoffs even when not going with speed on your board, is because of its excellent acceleration when you turn the kite backwards, and the profile has still more lift than Airblasts.
But if you are not skilled and don't get the kite forward while in the air - your landing and airtime will suck.
This is much easier with the Wook.
You could also call the Skoop style an "Airblast style with more low end" which is exactly what it is.
Bruno's latest kitedesign before the Skoop (1's) when he started Takoon, was the Airblast - and when seeing the success of this one, but with some complaining about the low end of the Airblast - the next step would be to make an improved Airblast of course.
Same kitestyle, but more power at lower speeds.
The Skoop2 has been most refined regarding acceleration, and is tougher than the 1's - besides having an even more direct and hard feeling (Airblast feeling, with more low end).
Because so many, also Pro riders, wanted a "Takoon style" kite - which was a little steadier in the jumps and to use for waveriding also - the Wook was developed.
Of course all brands have different styles, and some brands has this "Takoon/Airblast" style.
Maybe it should be called "Legaignoux" style, as this is where this style comes from (2000-2001 Airblast style).
Last year the Airush Lift and Naish X2 had similar Airblast styles, just slightly different in some aspects - so they are used of many brands, because of this "kitestyle"s success.
I myself really prefer the Skoop2 style - which is just what I like and love.
But many prefers the Wook style - which is still the "Legaignoux" style - but with a more stable and forgiving kite, that relaunches fast.
They both turns fast, so here there is no difference.
Older medium AR kites tends to turn much slower than the high AR kites.
This is not the case today, as design has progressed, and medium AR kites are not only for intermediates anymore.
Hope this explains the history/style !