CaptK6, I'm sure my understanding is very elementary, but I think this is the basic function
Rotating Barrel - at least in the PX4:
Upon firing, the recoil of the slide allows a lug on the locking block to engage a groove in the barrel. As the lug rides the groove, the recoil forces are distributed by a rotation of the barrel, rotating the recoil forces more in a straight line.
Browning-style Tilting Barrel - like most current designs:
Upon firing, for a few millimeters of rearward travel, the barrel remains locked to the slide. This allows the barrel to maintain accuracy until the bullet leaves the barrel, at which point the barrel tilts downward, allowing recoil forces to dissipate.
I think either system can potentially be more accurate than any shooter without a rest.
Beretta PX4 .40 S&W - Beretta 92FS 9x19 Para - Rock Island Armory GI 1911 .45 ACP - Colt 1968 Detective Special .38 Spc. - Ruger LCP .380 ACP - Daniel Defense M4V1 Carbine 5.56x45 - Alpine Industries M1 Carbine .30 - Steyr-Mannlicher M1895 8x56 - Ruger 10/22 .22LR - Remington 870 Express Tactical 12GA - 1943 Izhevsk Mosin-Nagant M91/30 7.62x54R