Large language models have become popular over a short period of time because they can generate text that resembles human writing across various domains and tasks. The popularity and breadth of use also put this technology in the position to fundamentally reshape how written language is perceived and evaluated. It is also the case that spoken language has long played a role in maintaining power and hegemony in society, especially through ideas of social identity and ``correct'' forms of language. But as human communication becomes even more reliant on text and writing, it is important to understand how these processes might shift and who is more likely to see their writing styles reflected back at them through modern AI. We therefore ask the following question: \textit{who} does generative AI write like? To answer this, we compare writing style features in over 150,000 college admissions essays submitted to a large public university system and an engineering program at an elite private university with a corpus of over 25,000 essays generated with GPT-3.5 and GPT-4 to the same writing prompts. We find that human-authored essays exhibit more variability across various individual writing style features (e.g., verb usage) than AI-generated essays. Overall, we find that the AI-generated essays are most similar to essays authored by students who are males with higher levels of social privilege. These findings demonstrate critical misalignments between human and AI authorship characteristics, which may affect the evaluation of writing and calls for research on control strategies to improve alignment.