This paper studies handwritten digit recognition methods with Convolutional Neural Networks (CNN) while performing a performance comparison with EfficientNetV2. The investigators applied the EMNIST dataset for model education and performance testing before using it to examine the model generalization characteristics through HASYv2 dataset analyses. The research examines key obstacles in handwritten digit recognition through multiple aspects such as different writing styles and diverse dataset characteristics as well as inefficient computing capabilities. The research evaluates enhanced accuracy through preprocessing methods along with model optimization methods. The research data reveals CNN provides excellent performance on EMNIST although it falls short on HASYv2 whereas EfficientNetV2 extracts superior features yet requires more computation power. The evaluation reveals the effective features and challenging aspects of both models so researchers can focus on developing hybrid structures and growing datasets for actual handwriting recognition systems in OCR applications and banking and automated document processing fields.