The one with the resistor will exhibit a damped oscillation, and the one with the capacitor has no damping. As to when you use one or the other, that depends upon what you are trying to accomplish with the circuit. You tell me. :???:
In the first place, neither of those circuits is resonant at 1000 Hz. You would have to crank up the frequency to 50329 for that to happen. Neither of those circuits will decay because they are driven by a voltage source. The impedance of the first circuit at 1000 Hz is R+0.0629j, and the second circuit is -15.8526j . You will have to decide where to use them.