Don't forget the curvature of the earth. The fired one will hit .0001 seconds later, or something. 
For the distance a bullet travels the curvature of the earth is insignificant.
Ok, a lot of variables involved.
If you take out friction of air and no air currents, assume a perfectly flat area, the distance the bullet flies is in significant to the earth's curvature, the bullet dropped was dropped at the instant the fired bullet left the barrel, and both bullets started at the exact same height, then they would both hit the ground at the same time. This is becuse gravity is a constant force downward. Both objects have the same downward force vector, no matter what horizontal force vector there is. In fact, assume the above conditions the bullet fired will hit the ground with the same horizontal velocity as it had when it left the barrel.
If the answer is that both DO hit the ground at the same time, I would have to see that to believe it. Is there not a huge variable in the amount of energy released by the casing? Different bullets fired horizontally will go further than others, there is no way all bullets fired in this way would hit the ground at the same time....
Or did you just blow my mind?
See my above explaination...
I will add, with the above conditions, if you fire multiple bullets you need them to leave the barrels at exactly the same time. Since there will be different FPS some will have to be fired slightly ahead of others in order for that to happen

But yes, if you fired all at the same time they would all hit the ground at the same time. The horizontal force from the chemicals has nothing to with the vertical force from the earth.