Humans are influenced by how information is presented, a phenomenon known as the framing effect. Prior work suggests that LLMs may also be susceptible to framing, but it has relied on synthetic data and did not compare to human behavior. To address this gap, we introduce WildFrame - a dataset for evaluating LLM responses to positive and negative framing in naturally-occurring sentences, alongside human responses on the same data. WildFrame consists of 1,000 real-world texts selected to convey a clear sentiment; we then reframe each text in either a positive or negative light and collect human sentiment annotations. Evaluating eleven LLMs on WildFrame, we find that all models respond to reframing in a human-like manner ($r\geq0.52$), and that both humans and models are influenced more by positive than negative reframing. Notably, GPT models are the least correlated with human behavior among all tested models. These findings raise a discussion around the goals of state-of-the-art LLM development and whether models should align closely with human behavior, to preserve cognitive phenomena such as the framing effect, or instead mitigate such biases in favor of fairness and consistency.