It is a consideration... the more power an amp gets through the input signal, the easier it is for the amp to amplify the signal, thus you'll get more sound. Its also helpful for rejecting noise.

There are also other factors involved though, not just preamp output power. The way things are tuned, amplifier output power, wirring configuration, the vehicle its in, the damping applied to the car....... there are a ton of things that contribute to one being "louder" than another.