So the conductance is not 1/R it is R/ (R^2 + (wL)^2) which implies that the resistance for the parallel case is much greater than for the series case - as you would expect.
The main loss in a capacitor is the dielectric loss. This can be represented by a parallel resistor. But inductors have copper loss and possibly magnetic losses such as eddy currents.
So in a RLC circuit, most of the loss is due to the inductor.