Large Language Models (LLMs) excel in text generation and understanding, especially in simulating socio-political and economic patterns, serving as an alternative to traditional surveys. However, their global applicability remains questionable due to unexplored biases across socio-demographic and geographic contexts. This study examines how LLMs perform across diverse populations by analyzing public surveys from Chile and the United States, focusing on predictive accuracy and fairness metrics. The results show performance disparities, with LLM consistently outperforming on U.S. datasets. This bias originates from the U.S.-centric training data, remaining evident after accounting for socio-demographic differences. In the U.S., political identity and race significantly influence prediction accuracy, while in Chile, gender, education, and religious affiliation play more pronounced roles. Our study presents a novel framework for measuring socio-demographic biases in LLMs, offering a path toward ensuring fairer and more equitable model performance across diverse socio-cultural contexts.