While social media has transformed political campaigning and is widely utilized by non-state actors, there remains limited insight into how these tools are employed by interest groups compared to traditional offline methods. This study addresses this gap by examining the argumentation strategies groups adopt when communicating online versus offline. Specifically, it conducts an AI-guided experiment that explores how groups prefer to convey their positions, focusing on both social media posts and emails to elected representatives. Using text-based treatments of these messages, experimentally manipulated with a Large Language Model, we examine how interest associations and firms prioritize lobbying messages that differ in attributes. Our conjoint experiments are run in 10 different countries, allowing for a comparative analysis of how advocacy strategies vary across diverse political and cultural contexts. The findings contribute to a more nuanced understanding of the strategic use of on- and offline communication tools by interest groups and have important implications for understanding advocacy strategies in the digital age.