Atmospheric water harvesting (AWH) technologies have the potential to enable decentralized water supply in remote regions where infrastructure is lacking. Sorption-based AWH, specifically, could further expand global water accessibility by leveraging advances in novel sorbent development and device design toward enabling high water productivity over diverse climate conditions. Metal-organic framework (MOF) and hygroscopic hydrogels are promising sorbents that show superior water uptake at low and high humidity conditions, respectively. To guide materials optimization, a generalized thermodynamic framework, which predicts the theoretical efficiency limits of AWH based on fundamental material properties and device operating conditions, is highly valuable. In this work, we first propose a generalization to previous AWH thermodynamic models that considers the continuously increasing isotherms of hydrogels. Next, we apply the generalized model to predict the thermodynamic limits of hydrogel-based AWH devices at various desorption temperatures and humidity conditions. Finally, we capture the effect of salt loading on the water uptake and maximum AWH efficiency of hydrogel, based on the experimentally characterized isotherms of PAM hydrogels loaded with LiCl. Our results show that the theoretical limit for AWH efficiency using hydrogel could exceed that of MOF-303 by up to 30%, for relatively humid ambient conditions (RH>40%). For any ambient RH, the maximum thermal efficiency of hydrogel-based AWH can be improved by increasing the desorption temperature until a humidity-dependent optimum is reached. Moreover, we show that salt loading has the potential to further enhance the upper-bound efficiency of hydrogel-based AWH devices, particularly at high ambient humidity, in addition to significance increases in the uptake. These findings provide fundamental insights for the material selection and device optimization of next-generation sorption-based AWH technology, particularly by highlighting the relative merits of MOF, pure hydrogel, and salt-impregnated hydrogel, under various climate and device operating conditions.