This study presents a novel dual-perspective approach to analyzing user reviews for ChatGPT and DeepSeek on the Google Play Store, integrating lexicon-based sentiment analysis (TextBlob) with deep learning classification models, including Convolutional Neural Networks (CNN) and Bidirectional Long Short Term Memory (Bi LSTM) Networks. Unlike prior research, which focuses on either lexicon-based strategies or predictive deep learning models in isolation, this study conducts an extensive investigation into user satisfaction with Large Language Model (LLM) based applications. A Dataset of 4,000 authentic user reviews was collected, which were carefully preprocessed and subjected to oversampling to achieve balanced classes. The balanced test set of 1,700 Reviews were used for model testing. Results from the experiments reveal that ChatGPT received significantly more positive sentiment than DeepSeek. Furthermore, deep learning based classification demonstrated superior performance over lexicon analysis, with CNN outperforming Bi-LSTM by achieving 96.41 percent accuracy and near perfect classification of negative reviews, alongside high F1-scores for neutral and positive sentiments. This research sets a new methodological standard for measuring sentiment in LLM-based applications and provides practical insights for developers and researchers seeking to improve user-centric AI system design.