There's a reason why they have both coils with only one winding, in one side of the mains (which reviews here refer to as "half" a coil), and those with two windings, one for each side of the mains (a "full" coil).
The ones in only one side of the mains are, along with X-class capacitors, for differential-mode (live-to-neutral) noise filtering. You can expect these to have an inductance of up to a few hundred microhenries (µH), which won't cause a significant voltage drop, even at 63Hz (semi-regularly given as the upper end of the frequency range, though most PSUs can probably go quite a bit higher without problems) and with several amps of current draw. The downside, however, is that they are not efficient at common-mode (between live/neutral and earth) noise filtering, as Y-class capacitors are by necessity much smaller than X-class, as current flow in the earth wire has to be limited to a safe level.
The ones with windings for each side of the mains are those used for common-mode noise filtering. One with a ferrite EE-25 core that I'm looking at right now, bearing the "Ever-power" branding as commonly seen in PSUs made by K-Mex, is rated for 13 millihenries. The reactance you'd get from putting a 13mH differential-mode inductor in series with the mains is:
2*pi*60*0.013 = 4.9Ω
Now obviously that would be a hell of a lot to put in line with the PSU input, as several volts would be dropped. That inductor would also have to have a very large core to avoid saturating under the load current.
Fortunately for PSU engineers, there's a trick that sidesteps both problems: Build an inductor with two windings on a common core, and wire it up so that the load current induces equal and opposite magnetic fields in each winding. These cancel each other out and result in zero net magnetic field, preventing saturation of the core. And because the field can no longer form (unless someone miswires the inductor or the PSU), the inductance as far as the load is concerned is 0mH. This does also mean that they are ineffective against differential-mode noise, but using both them and the differential-mode inductors in conjunction is still a win-win for cost and performance.
