This research explores the factors individuals consider when choosing an information search source, particularly the shift from traditional search engines to Generative AI platforms like ChatGPT, focusing on how the complexity of search tasks aligns with the cognitive capacities of these technologies. Drawing on Task-Technology Fit theory, this study shows that user satisfaction depends on the fit between task complexity and the cognitive capacity of a search source. Through experimental design, the study examines the impact of this alignment on user satisfaction across various task complexities. This investigation contributes to understanding the optimal use of search technologies, addressing the dynamics between technology capabilities and user needs in the evolving landscape of information search behavior.