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Understanding actions in videos remains a significant challenge in computer vision, which has been the subject of several pieces of research in the last decades. Convolutional neural networks (CNN) are a significant component of this topic and play a crucial role in the renown of Deep Learning. Inspired by the human vision system, CNN has been applied to visual data exploitation and has solved various challenges in various computer vision tasks and video/image analysis, including action recognition (AR). However, not long ago, along with the achievement of the transformer in natural language processing (NLP), it began to set new trends in vision tasks, which has created a discussion around whether the Vision Transformer models (ViT) will replace CNN in action recognition in video clips. This paper conducts this trending topic in detail, the study of CNN and Transformer for Action Recognition separately and a comparative study of the accuracy-complexity trade-off. Finally, based on the performance analysis's outcome, the question of whether CNN or Vision Transformers will win the race will be discussed. [ABSTRACT FROM AUTHOR]