Personalized gamification aims to address shortcomings of the one-size-fits-all (OSFA) approach in improving students' motivations throughout the learning process. However, studies still focus on personalizing to a single user dimension, ignoring multiple individual and contextual factors that affect user motivation. Unlike prior research, we address this issue by exploring multidimensional personalization compared to OSFA based on a multi-institution sample. Thus, we conducted a controlled experiment in three institutions, comparing gamification designs ("OSFA" and "Personalized" to the learning task and users' gaming habits/preferences and demographics) in terms of 58 students' motivations to complete assessments for learning. Our results suggest no significant differences among OSFA and Personalized designs, despite suggesting user motivation depended on fewer user characteristics when using personalization. Additionally, exploratory analyses suggest personalization was positive for females and those holding a technical degree, but negative for those who prefer adventure games and those who prefer single-playing. Our contribution benefits designers, suggesting how personalization works; practitioners, demonstrating to whom the personalization strategy was more or less suitable; and researchers, providing future research directions.