All wars up until the 1850's would be much the same. The telegraph was developed during this time. This was the first time communication speed was comparable to the speed of light. Even so, it was still very slow for a while. The first transatlantic telegraph message took seventeen hours to transmit (in 1858). Things quickly picked up. By 1866, transatlantic telegraph messages could be exchanged at eight words per minute. By contrast, even at peak speeds, a message traveling at the speed of sound would take four and a half hours to go from New York to London.
It would be impossible to replace light speed communication with sound because sound dissipates very fast compared to electromagnetic radiation, so it would take an unbelievable amount of power to produce messages in sound which can be heard more than just few dozen miles away. Not to mention the damage done to the ears of those near the source.
In the real universe, rapid messaging is essential between military units within a theater. Spread across hundreds of miles, communication at the speed of sound would be on the scale of hours. I do not think this would affect tactics too much, except each unit would be in the habit of communicating large amounts of information all at once so their comrades have as much information as possible, without the need for back and forth communication. Those sending messages would be better at making messages detailed and clear. Plans would be laid out in great detail with many contingencies to limit the need for real-time communication.
Drones and the like would be pretty much impossible. You couldn't react fast enough to make it useful. Even computers would be noticeably slower. That said, modern computer technology is very fast, so weapons with onboard computers may have small, modern-looking computers which are as slow as computers in the seventies.
There is one thing that would work better: sonar. Sound under water has a greater range than sound in air. It's not great, but active sonar between submarines works on the range of tens of nautical miles. if this communication was at what we would call the speed of light, then fast communication is possible through sonar. For instance, a system of buoys twenty nautical miles apart could be arranged across the Atlantic ocean. If each buoy receives a sonar message and then re transmit it. If each transmission takes a minute, then you could send a message from New York to London in less than three hours, a little faster.
If this situation were reality, technologies would be developed to take advantage of the fast speed of sounds. We would develop better microphones, louder speakers, and longer under water communication. I disagree that sound could be used as a weapon more effectively in this universe than here. The speed of sound is the speed at which molecules transfer energy. I don't think that over the range of several hundred feet we would really notice a difference. Even at large distances, you would have to pay close attention to notice a difference.
There are other implications to faster than light communications. There is potential to violate causality: you could observe an effect before a cause. This is not good, and very complicated. Unfortunately, I am not a good enough theorist to come up with any specific examples.