Recognizing Vietnamese handwritten text poses significant challenges due to complex diacritics, tonal variations, and limited large-scale annotated datasets. Traditional deep learning-based OCR methods, such as CRNNs designed specifically for Vietnamese handwriting, have demonstrated strong accuracy and low word error rates when trained on targeted data. In contrast, Vision-based Large Language Models (Vision-LLMs) offer broader document understanding, multimodal perception, and downstream capabilities like question answering and content interpretation. However, these models often struggle with domain adaptation, linguistic nuances, and computational efficiency, especially in the context of Vietnamese script. This paper presents a systematic comparison of OCR-specific models and Vision-LLMs for Vietnamese handwriting recognition, examining model architecture, data dependencies, recognition performance, linguistic handling, flexibility, and deployment feasibility. The results indicate that while OCR-specialized models excel in accuracy and resource efficiency within narrow domains, Vision-LLMs provide greater adaptability across tasks - albeit with higher resource demands and sensitivity to script details. Finally, we propose future directions, including hybrid approaches, dataset expansion, and optimization strategies, to advance robust and versatile Vietnamese handwriting recognition systems.