Thank you, crutschowNot really.
The first adds resistance to the diode, which significantly reduces efficiency, and only damps the ringing from the diode capacitance, not from any other stray capacitance.
You need the second circuit, with the resistance in series with the capacitor, to absorb the tank energy.
The added capacitance swamps the stray capacitance so that most of the energy is absorbed in the resistor.