We have compared the prediction capability of two types of Sun-Earth connection models: (1) ensemble of physics-based shock propagation models (STOA, STOA-2, ISPM, and HAFv.2) and (2) empirical CME propagation (CME-ICME and CME-IP shock) models. For this purpose, we have selected 38 near-simultaneous pairs of coronal mass ejections (CMEs) and metric type II radio bursts. By applying the adopted models to these events, we have estimated the time difference between predicted and observed arrivals of interplanetary (IP) shocks and ICMEs at the Earth or L1. The mean absolute error of the shock arrival time (SAT) within an adopted window of ¿24 hours is 9.8 hours for the ensemble of shock propagation models, 9.2 hours for the CME-IP shock model, and 11.6 hours for the CME-ICME model. It is also found that the success rate for all models is about 80% for the same window. The results imply that the adopted models are comparable in their prediction of the arrival times of IP shocks and interplanetary CMEs (ICMEs). The usefulness of these models is also discussed in terms of real-time forecasts, underlying physics, and identification of IP shocks and ICMEs at the Earth.