Are typical computer power supply units leading or lagging power?
It's not so much a case of leading or lagging.  On a non-PFC power supply, the circuit consists of a bridge rectifier, followed by a large bulk capacitor.  The cap charges and droops between the AC line cycles.  During a potentially large portion of the AC line cycle the bridge doesn't conduct because the cap voltage is still above the rectified AC line voltage.  Right near the peak of the line the line voltage exceeds the cap voltage, and all of the current flows into the cap during that small conduction angle.

So it doesn't look strictly inductive or capacitive, but it does generate large line harmonics.  That's really what "power factor correction" standards regulate. It's not really the power factor, but the harmonics.  The huge peak currents compared to the average current draw is the issue for the utilities.