One benefit of an external crossover is that the high pass filtering is done before the signal enters the power amp. Removing low frequencies from the signal sent to the power amp results in less amp distortion, and more power for the speakers.
By the way, the problem with the Harrison filters is that to achieve the crossover frequency you want, the input impedance of the power amp must be figured into the equation that determines the capacitor value required to achieve that crossover frequency.