1st, you must define what you mean 'punch' and 'authority'. These are subjective terms that I do not see being defined in a quantitive/meaningful manner. However, the degree of any effect depends entirely on the amplitude(volume/SPL) at the specific frequency band[that you consider to be punch] that you experience at the listening position. Ultimately, what is important[and relevant] to the situation is the frequency response at your listening position, the SPL within required bandwidth, low frequency dispersion(most LF devices are omnidirectional, but exceptions exist such as dipole and cardoid systems--but this ultimately effects the other two factors) and the integration with the main speakers at Fc(frequency crossover) between the sub(s) and main(s). Your room acoustics will have a very big effect, as will the placement of the speakers in interaction with this issue.
-Chris