Robot-assisted minimally invasive surgery, such as through the da Vinci systems, improves precision and patient outcomes. However, da Vinci systems prior to da Vinci 5, lacked direct force-sensing capabilities, forcing surgeons to operate without the haptic feedback they get through laparoscopy. Our prior work restored force sensing through machine learning-based force estimation for the da Vinci Research Kit (dVRK) Classic. This study extends our previous method to the newer dVRK system, the dVRK-Si. Additionally, we benchmark the performance of the learning-based algorithm against baseline methods (which make simplifying assumptions on the torque) to study how the two systems differ. Results show the learning-based method achieves an average root-mean-square-error (RMSE) of 5.21\%, for the dVRK-Si, which is comparable to the dVRK Classic. In both systems, the learning-based method outperforms baselines, but the difference is much larger in the dVRK-Si. Nonetheless, dVRK-Si force estimation accuracy lags behind the dVRK Classic, with RMSE 2 to 3 times higher. Further analysis reveals poor PID control in the dVRK-Si. We hypothesize that this is due to the lack of gravity compensation, as unlike the dVRK Classic, the dVRK-Si is not mechanically balanced. This study advances the understanding of learning-based force estimation and is the first work to characterize the dynamics of the new dVRK-Si system.