The rapid advancements in large language models (LLMs) have significantly improved their ability to generate natural language, making texts generated by LLMs increasingly indistinguishable from human-written texts. While recent research has primarily focused on using LLMs to classify text as either human-written or machine-generated texts, our study focuses on characterizing these texts using a set of linguistic features across different linguistic levels such as morphology, syntax, and semantics. We select a dataset of human-written and machine-generated texts spanning 8 domains and produced by 11 different LLMs. We calculate different linguistic features such as dependency length and emotionality, and we use them for characterizing human-written and machine-generated texts along with different sampling strategies, repetition controls, and model release dates. Our statistical analysis reveals that human-written texts tend to exhibit simpler syntactic structures and more diverse semantic content. Furthermore, we calculate the variability of our set of features across models and domains. Both human- and machine-generated texts show stylistic diversity across domains, with human-written texts displaying greater variation in our features. Finally, we apply style embeddings to further test variability among human-written and machine-generated texts. Notably, newer models output text that is similarly variable, pointing to a homogenization of machine-generated texts.