I think the very fact that they could have rocks thrown at them prevented them from using their war balloons. I believe that they used the Drill because they hadn't yet finished construction on them, the giant balloons. Also from the show, we get to see how much damage "rocks" actually do when aimed right.

Another reason might be psychological, seeing as how the Fire Nation enjoys using psychological warfare. With a Drill they literally break through their opponents defenses in a way that would make one more susceptible to fear because nothing they do can penetrate the Drill. While with the balloons they can at least take a few down.

Or it was already planned out, and before common sense, on using the balloons, sets in; the Princess shows up and demands to watch. You just don't say no to Azula.

And yes, it was a good episode.