The aim of this study is to show that the measures derived from Electrocardiogram (ECG) signals many a time perform better than the same measures obtained from heart rate (HR) signals. A comparison was made to investigate how far the nonlinear symbolic dynamics approach helps to characterize the nonlinear properties of ECG signals and HR signals, and thereby discriminate between normal and congestive heart failure (CHF) subjects. The symbolic dynamics calculations performed on normal and CHF ECG and HR signals showed significant differences in the symbol-sequence histogram statistics and complexity measures (modified Shannon entropy (MSE) and multi-valued Lempel-Ziv complexity (MLZC)) of symbol sequences between the two groups. The ability of these complexity measures to discriminate normal from CHF subjects was evaluated using receiver operating characteristic (ROC) plots. It is found that MSE and MLZC measures obtained from ECG signals performed better than the same measures derived from HR signals of the same subjects.