Kiteboards with very thin tips are more maneuvering than the ones with wide tips (these are more stable during a ride).
A perfect balance is needed so the board is not either too shaky or too stubborn. Besides, wide tips will be splashing while doing chops. Boards with narrow tips are not that good for approaches because the less effective surface of an edge is in water.
Besides all of the mentioned above, length to width ratio is very important too: middle width defines the ability to approach. Narrow boards go upwind way too worse than the wide ones (with the same rider’s weight obviously). Nowadays every producing company has this ratio measured very precisely and experiments with this ratio are very old-fashioned, but…
It’s obvious that narrow boards are more maneuvering, good for spins, but worse in stability and release before a trick than the long ones (you can feel it best when doing a wakestyle).
The profile neither should be too narrow (to be able to go upwind comfortably and accumulate more energy before a take-off) nor should be too wide (it becomes too clumsy).
Of course the length of a board should match the rider’s height and, accordingly, the width of the rider's stand to avoid the situation when the rider’s stand is too narrow to sit down. This will negatively affect the rider's knees and your riding experience. In addition, it should be understood that a wide stand simplifies riding upwind but makes doing tricks harder (especially with rotations).
All in all, that all is subjectively and personally and sometimes that all is just a matter of habit.