The sound of a police car, fire engine, and ambulance has remained almost unchanged in the US for the last 50 years or so. The delivery systems have evolved from analog klaxons to electronic ones, so they are capable of issuing the now familiar "quick-hoots" or "burst of static honks". Nice, as it's not always a big enough emergency to warrant running the sirens at full blast and forcing people down the road to pull over.
When each vehicle runs the full siren, though, they're pretty distinctive in most places, allowing drivers to tell what sort of vehicle is coming. Fire response is most distinctive, with a deep, drawn wail, often accented by the regular horn being hit every 10 seconds or so. Police and ambulance sound kind of the same, but the ambulance will tend to remain for longer durations on a single, steady sound, while police will modulate all over the place.
Differences between the states are pretty minimal. Plus, they don't want to intruduce changes unless necessary, as they want people aware of what's going on at all times with emergencies. Technically, the core sound of the emergency siren hasn't changed for almost 3 generations.
Here's a vid that highlights the differences well enough:
