Counterspeech is a targeted response to counteract and challenge abusive or hateful content. It effectively curbs the spread of hatred and fosters constructive online communication. Previous studies have proposed different strategies for automatically generated counterspeech. Evaluations, however, focus on relevance, surface form, and other shallow linguistic characteristics. This paper investigates the human likeness of AI-generated counterspeech, a critical factor influencing effectiveness. We implement and evaluate several LLM-based generation strategies, and discover that AI-generated and human-written counterspeech can be easily distinguished by both simple classifiers and humans. Further, we reveal differences in linguistic characteristics, politeness, and specificity. The dataset used in this study is publicly available for further research.