The capacitor will slow down the edges when the GPIO16 tries to drive it so one would tend to think that the ESP-12S module may have a higher value capacitor and that is what gives rise to the slower edges on the ESP-12S module.
The bit that is puzzling is that the ESP-12E shows the 'normal' behaviour where the GPIO16 outputs a fixed width pulse to do the reset (wakeup) whereas the pulse on the ESP-12S seems to be switched off as soon as the reset is sensed, and the waveform starts to rise immediately. That would indicate that either the slower edge (higher capacitance) is upsetting the reset behaviour or that there is real difference between the chips behaviour in handling GPIO16 during wake ups.
In principle, if the reset is still seen by the ESP-12S then it should still work OK, but you indicate that you see intermittent problems. If one wanted to check further then one could try putting a buffer between GPIO16 and the reset to speed up the discharge.