Ehhh, not really.
It depends on the player. A quick tight cross works better for a quicker player. They don't really need to create much movement from their defender to get by them, so quick moves work better.
Wider crossovers work for players who have strength and want to get their opponent more off-balance before making their counter.
I don't think so. A tight crossover is always better. The distance traveled by the ball is shorter, making the crossover quicker, regardless of whether you're a slow or quick player. Also, width of crossover is not related to creating movement, as that is accomplished by your legs and your hips, and not with the ball. Have you not seen Curry break ankles and send his man to the floor with his crosses? Tight crosses also allows you to more efficiently transfer your momentum forward, instead of having to drag the ball from 4 feet away.
Here's a bunch of players discussing it.
https://www.youtube.com/watch?v=sbfHghWC99U