The use of parametric linear mixed models and generalized linear mixed models to analyze longitudinal data collected during randomized control trials (RCT) is conventional. The application of these methods, however, is restricted due to various assumptions required by these models. When the number of observations per subject is sufficiently large, and individual trajectories are noisy, functional data analysis (FDA) methods serve as an alternative to parametric longitudinal data analysis techniques. However, the use of FDA in randomized control trials, is rare. In this paper, the effectiveness of FDA and linear mixed models was compared by analyzing data from rural persons living with HIV and comorbid depression enrolled in a depression treatment randomized clinical trial. Interactive voice response (IVR) systems were used for weekly administrations of the 10-item Self-Administered Depression Scale (SADS) over 41 weeks. Functional principal component analysis and functional regression analysis methods detected a statistically significant difference in SADS between telphone-administered interpersonal psychotherapy (tele-IPT) and controls but, linear mixed effects model results did not. Additional simulation studies were conducted to compare FDA and linear mixed models under a different nonlinear trajectory assumption. In this clinical trial with sufficient per subject measured outcomes and individual trajectories that are noisy and nonlinear, we found functional data analysis methods to be a better alternative to linear mixed models.