The internal force antagonism (IFA) problem is one of the most important issues limiting the applications and popularization of redundant parallel robots in industry. Redundant cable-driven parallel robots (RCDPRs) and redundant rigid parallel robots (RRPRs) behave very differently in this problem. To clarify the essence of IFA, this study first analyzes the causes and influencing factors of IFA. Next, an evaluation index for IFA is proposed, and its calculating algorithm is developed. Then, three graphical analysis methods based on this index are proposed. Finally, the performance of RCDPRs and RRPRs in IFA under three configurations are analyzed. Results show that RRPRs produce IFA in nearly all the areas of the workspace, whereas RCDPRs produce IFA in only some areas of the workspace, and the IFA in RCDPRs is milder than that RRPRs. Thus, RCDPRs more fault-tolerant and easier to control and thus more conducive for industrial application and popularization than RRPRs. Furthermore, the proposed analysis methods can be used for the configuration optimization design of RCDPRs.