Control over an avatar in virtual reality can improve one's perceived sense of agency and embodiment towards their avatar. Yet, the relationship between control on agency and embodiment remains unclear. This work aims to investigate two main ideas: (1) the effectiveness of currently used metrics in measuring agency and embodiment and (2) the relationship between different levels of control on agency, embodiment, and cognitive performance. To do this, we conducted a between-participants user study with three conditions on agency ($\mathrm{n}=57$). Participants embodied an avatar with one of three types of control (i.e., Low - control over head only, Medium - control over head and torso, or High - control over head, torso, and arms) and completed a Stroop test. Our results indicate that the degree of control afforded to participants impacted their embodiment and cognitive performance but, as expected, could not be detected in the self-reported agency scores. Furthermore, our results elucidated further insights into the relationship between control and embodiment, suggesting potential uncanny valley-like effects. Future work should aim to refine agency measures to better capture the effect of differing levels of control and consider other methodologies to measure agency.