In terms of popularity, it is difficult to definitively say which band is more popular as it depends on various factors such as the criteria used to measure popularity, the time frame being considered, and the specific region or demographic being examined. Both bands have achieved widespread recognition and success, with Aerosmith having a longer career and R.E.M. having a significant influence on alternative rock.
According to various sources and metrics, Aerosmith has a larger social media following and has received more Grammy Awards than R.E.M. However, R.E.M. has been ranked higher on lists such as Rolling Stone's "500 Greatest Albums of All Time" and VH1's "100 Greatest Artists of All Time."
Overall, both Aerosmith and R.E.M. are highly regarded and influential rock bands, with their popularity varying based on different measures and contexts.