Computer power supplies often have "power factor correction" features which raise the power factor in use to levels close to resistive loads (1). I'm curious what, in the absence of power factor correction, power supply loads would be. (Switching-mode power supplies use both inductors and capacitors; I'm not sure what their load looks like on the AC side though)
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.
The above image shows a simple non-PFC switch mode power supply. This one would probably not be used as a computer PSU as it's low power, but it is sufficient to illustrate the point.
The mains is rectified to charge a capacitor, and then this high voltage DC rail is used to power the converter, which in this case is a simple flyback converter, but there are several other designs.
The capacitor is chosen to be sufficiently large that there is little ripple on it: as a result the rectifier can only conduct near the peak of the mains.
The result of this is not that the current leads or lags the voltage, but that the current is non-sinusoidal with peaks of current near the peaks of the voltage. This introduces significant harmonic distortion.
To add PFC on most power supplies, a second stage is added before this capacitor which shapes the current to follow the shape of the mains voltage. This is typically a boost converter as shown below.