This comes up over and over again. The speed of sound in air at sea level at 20 degrees C (about 68 degrees F) is 343 m/s or about 767 MPH. If the siren sound is coming towards you at 767 MPH and you're going 80 MPH in the same direction, you can see how "outdriving" the siren is not going to happen.
What happens is that the engine noise, airflow noise, tire noise etc go up the faster you drive, and make it more difficult to hear things around you including sirens, when the sound pressure of the siren sound is the same as or lower than the sound pressure of noise inside the car. Also, sound pressure varies with distance so a siren half a mile back is not going to be very loud in any case. But you're not "outdriving" it.
Since most of this interior vehicle noise is toward the higher frequency range, using something like a Rumbler might help. Also, using something like a Q or Grover horns which are relatively louder might help. But a 200 watt siren is only a moderate improvement over 100 watts. If you double the acoustic power in watts, you get only a 3 dB or 1.41x (41%) increase in sound pressure and 1.23x (23%) increase in perceived loudness.
So, a 200 watt siren will seem about 23% louder than a 100 watt siren, at the same distance. But you're not going to outrun or outdrive the sound unless you're in a jet. Then it's called breaking the sound barrier.
http://www.sengpielaudio.com/TableOfSoundPressureLevels.htm