Previous research has shown that using buckling-restrained braces (BRBs) at hinged wall (HW) base (HWBB) can effectively mitigate lateral deformation of steel moment-resisting frames (MRFs) in earthquakes. Force-based and displacement-based design methods have been proposed to design HWBB to strengthen steel MRF and this paper comprehensively compares these two design methods, in terms of design steps, advantages/disadvantages, and structure responses. In addition, this paper investigates the building height below which the HW seismic moment demand can be properly controlled. First, 3-story, 9-story, and 20-story steel MRFs in the SAC project are used as benchmark steel MRFs. Secondly, HWs and HWBBs are designed to strengthen the benchmark steel MRFs using force-based and displacement-based methods, called HWFs and HWBBFs, respectively. Thirdly, nonlinear time history analyses are conducted to compare the structural responses of the MRFs, HWBBFs and HWFs in earthquakes. The results show the following. 1) HW seismic force demands increase as structural height increases, which may lead to uneconomical HW design. The HW seismic moment demand can be properly controlled when the building is lower than nine stories. 2) The displacement-based design method is recommended due to the benefit of identifying unfeasible component dimensions during the design process, as well as better achieving the design target displacement.