The exponential growth of social media has created an urgent need for automated systems to analyze unstructured public sentiment in real time. This study compares a traditional Logistic Regression model using TF-IDF features with a deep learning Bidirectional Long Short-Term Memory (BiLSTM) architecture on a 10,000-tweet subset of the Sentiment140 dataset. Experimental results show that Logistic Regression outperformed BiLSTM, achieving an accuracy of 73.5% compared with 69.17%, while the deep learning model exhibited mild overfitting. These findings suggest that for medium-scale informal text data, classical machine learning with robust feature extraction can outperform more complex deep learning approaches. Finally, the trained models were integrated into an interactive web application using Streamlit and deployed on Hugging Face Spaces for public access.