I wonder if it could in any way be related to the version of the charging puck. I tried with an Apple original version charging stand (designed around the S0-S3 shape) and my wife's S3 charging puck from an S3.
It could be that S4 pucks are slightly flatter given the redesign of the back of the case..?
Actually, it's the other way around, the S4's pucks are more concave, because the back of the S4 has a taller dome than the earlier models.
The 44mm S4 back has a 1.52mm tall dome, while the 42mm S3 has a 1.07mm dome (or 1.22mm for the LTE model), to cite one comparison.
I noticed this by eyeball comparing a puck bundled with a new S4, vs. one from an S3, and Apple's dimensional drawings confirm it. That could be why some third-party accessories that don't employ the OE MFi puck are turning out to be incompatible with the S4.
Since the AirPower failure leaves Apple in an uncertain position regarding its own first-party multiple-device charger, it should just open up the Watch and AirPods to standard Qi charging as with the iPhones and save everyone a lot of headache.
And while they're at it, improve the communication handshake so that the indicator lights on
all standard Qi chargers function properly and acknowledge when an iPhone is fully charged. Some do, but most don't.
These kinds of uncertainly do users no favors.