Recent Large Language Models (LLMs) have shown the ability to generate content that is difficult or impossible to distinguish from human writing. We investigate the ability of differently-sized LLMs to replicate human writing style in short, creative texts in the domain of Showerthoughts, thoughts that may occur during mundane activities. We compare GPT-2 and GPT-Neo fine-tuned on Reddit data as well as GPT-3.5 invoked in a zero-shot manner, against human-authored texts. We measure human preference on the texts across the specific dimensions that account for the quality of creative, witty texts. Additionally, we compare the ability of humans versus fine-tuned RoBERTa classifiers to detect AI-generated texts. We conclude that human evaluators rate the generated texts slightly worse on average regarding their creative quality, but they are unable to reliably distinguish between human-written and AI-generated texts. We further provide a dataset for creative, witty text generation based on Reddit Showerthoughts posts.