Since the publication of The Case for Learned Index Structures in 2018, there has been a rise in research that focuses on learned indexes for different domains and with different functionalities. While the effectiveness of learned indexes as an alternative to traditional index structures such as B+Trees have already been demonstrated by several studies, previous work tend to focus on higher-level performance metrics such as throughput and index size. In this paper, our goal is to dig deeper and investigate how learned indexes behave at a micro-architectural level compared to traditional indexes. More specifically, we focus on previously proposed learned index structure ALEX, which is a tree-based in-memory index structure that consists of a hierarchy of machine learned models. Unlike the original proposal for learned indexes, ALEX is designed from the ground up to allow updates and inserts. Therefore, it enables more dynamic workloads using learned indexes. In this work, we perform a micro-architectural analysis of ALEX and compare its behavior to the tree-based index structures that are not based on learned models, i.e., ART and B+Tree. Our results show that ALEX is bound by memory stalls, mainly stalls due to data misses from the last-level cache. Compared to ART and B+Tree, ALEX exhibits fewer stalls and a lower cycles-per-instruction value across different workloads. On the other hand, the amount of instructions required to handle out-of-bound inserts in ALEX can increase the instructions needed per request significantly (10X) for write-heavy workloads. However, the micro-architectural behavior shows that this increase in the instruction footprint exhibit high instruction-level parallelism, and, therefore, does not negatively impact the overall execution time.