Question

which will hit the ground faster a ball thrown parallel to the ground or a ball drop from the same height as the ball

Answer 1

the ball that was the same height as the parallel ball

Answer 2

The question only makes sense if they're both released at the same time.

Both of them accelerate vertically at the same rate, and reach the same speed
at the same time. Both cover the same vertical distance in the same amount of
time, and both hit the ground at the same time.

And I don't think you even have to ignore air resistance to derive that fact.