My understanding of an X-pipe's function is as follows:
1) Creates an abrupt change of impedance for the pressure pulses from cylinder blow-down. This is the same function as performed by an exhaust "expander box" at the end of the collector, although with a lot less volume required. The change of impedance assures that the tuned length of the collector is correct. I would *not* expect an X-pipe to decouple the headers from the rest of the exhaust system the way that an expander box does, however.
2) Allows both banks to use both pipes. With a true dual exhaust, each bank has use of a single pipe. With an X-pipe, each bank has use of *BOTH* pipes. Double the cross-sectional area downstream of the collectors.
3) Provides "jet pump" effect for opposite bank. The blow-down phase of each cylinder's exhaust strokes occurs during the pump-down (post-blow-down) phase of the previous cylinder in the firing order. When the previous cylinder is in the opposite bank, the venturi effect of the blow down exhaust flow should help create a draw on the exhaust of the cylinder in the pump-down phase. This is the same principle in action as when exhaust flow is used to pull down crank case pressure.
4) Reduces exhaust noise. With a true dual exhaust, the entire acoustic energy generated by one bank of the engine comes out one pipe. By splitting the energy of each bank across two pipes, the peak intensity of each acoustic source (which is what we perceive as loudness) is reduced by at least 3 dB. The total acoustic power delivered is the same, but by "spreading it out", the perception of peak intensity is reduced.
5) Changes exhaust sound. With a true dual exhaust, each bank has a pulse output of "bang-wait-bang-wait-bang-bang-wait-wait" (X _ X _ X X _ _ ). The overlap of the two banks and the sequentially firing cylinders in each bank creates the beloved "throb" of a V8 exhaust. With an X-pipe, each pipe transmits each pulse from both banks ( x x x x x x x x )... Smoother and more Ferrari-esque, but not as much so as 180 degree headers (or a flat crank).
6) (Pure speculation... no test results) Changes *WHERE* behind the car the peak sound intensity is heard. In a true dual system, the alternating pulses from each bank create a two-element phased array that's out of phase. This *should* put peak sound intensity at 45 degrees off from directly behind the car. With an X-pipe and both outlets radiating in-phase, peak sound intensity should be directly behind the car.