The lack of double-differential cross-section (DDX) data for neutron production below the incident proton energy of 200 MeV hinders the validation of spallation models in technical applications, such as research and development of accelerator-driven systems (ADSs). The present study aims to obtain experimental DDX data for ADS spallation target materials in this energy region and identify issues related to the spallation models by comparing them with the analytical predictions. The DDXs for the (p,xn) reactions of natPb and 209Bi in the 100-MeV region were measured over an angular range of 30° to 150° using the time-of-flight method. The measurements were conducted at Kyoto University utilizing the FFAG accelerator. The DDXs obtained were compared with calculation results from Monte Carlo-based spallation models (INCL4.6/GEM, Bertini/GEM, JQMD/GEM, ISOBAR/GEM, CEM03.03, INCL4/ABLA, Bertini/ABLA, ISABEL/ABLA, INCL++/ABLA07, INCL++/GEMINI++, and INCL++/SMM) and the evaluated nuclear data library, JENDL-5. Comparison between the measured DDX and analytical values based on the spallation models and evaluated nuclear data library indicated that, in general, the CEM03.03 model demonstrated the closest match to the experimental values. Additionally, the comparison highlighted several issues that need to be addressed in order to improve the reproducibility of the proton-induced neutron-production DDX in the 100 MeV region by these spallation models and evaluated nuclear data library. To enhance the reproducibility of underperforming spallation models and evaluated nuclear data library, it is recommended to address each of the issues identified in this study.