The Plug-and-Play (PnP) framework was recently introduced for low-dose CT reconstruction to leverage the interpretability and the flexibility of model-based methods to incorporate various plugins, such as trained deep learning (DL) neural networks. However, the benefits of PnP vs. state-of-the-art DL methods have not been clearly demonstrated. In this work, we proposed an improved PnP framework to address the previous limitations and develop clinical-relevant segmentation metrics for quantitative result assessment. Compared with the DL alone methods, our proposed PnP framework was slightly inferior in MSE and PSNR. However, the power spectrum of the resulting images better matched that of full-dose images than that of DL denoised images. The resulting images supported higher accuracy in airway segmentation than DL denoised images for all the ten patients in the test set, more substantially on the airways with a cross-section smaller than 0.61cm$^2$, and outperformed the DL denoised images for 45 out of 50 lung lobes in lobar segmentation. Our PnP method proved to be significantly better at preserving the image texture, which translated to task-specific benefits in automated structure segmentation and detection.