Induction motors (IMs) play a pivotal role in various industrial applications, powering critical systems such as pumps, compressors, fans, blowers, and refrigeration and air conditioning systems. Monitoring the health of these IMs is essential for ensuring reliable operation. Numerous sensors, including vibration, current, temperature, acoustic, and power sensors, can be employed for their health monitoring. This article conducts a comprehensive comparative analysis of two widely used sensors—vibration and current, for classifying different health states of IMs, such as a healthy condition, bearing fault, and misalignment. The study employed deep learning techniques, specifically 1D and 2D convolutional neural networks, trained on raw data. Additionally, machine learning techniques, including random forest and XGBoost, were utilized and trained on features derived from preprocessed signals using fast Fourier transform and discrete wavelet decomposition. Comparative results indicated that vibration signals achieved remarkably high accuracy, nearly 100%, in detecting the investigated mechanical faults, while current signals, after signal processing and manual feature extraction, achieved an accuracy of 87.41%. These results demonstrate that, though current sensors are a viable alternative to vibration sensors, their performance can be affected by the type and degree of the considered faults. This study also highlights the attributes of vibration and current signals in the health monitoring of rotating machinery such as IMs.