Note: For those who have seen it, the famous demonstration of shooting a falling monkey is very relevant here...
...first some definitions:
In order for there to be an impact, at some time 
and 
must
be equal...
Since time cancels out of the equations, not only are the initial velocities equal, but so are the y components of the positions of the projectiles - all the time. Since they are both being accelerated by the same force, and both have the same initial conditions, their motion in the y direction will be exactly the same.