The hybrid nature of optoacoustic tomography (OAT) brings together the advantages of both optical imaging and ultrasound imaging, making it a promising tool for breast cancer imaging. It is advocated in the modern imaging science literature to utilize objective, or task-based, measures of system performance to guide the optimization of hardware design and image reconstruction algorithms. In this work, we investigate this approach to assess the performance of OAT breast imaging systems. In particular, we apply principles from signal detection theory to compute the detectability of a simulated tumor at different depths within a breast, for two different system designs. The signal-to-noise ratio of the test statistic computed by a numerical observer is employed as the task-specific summary measure of system performance. A numerical breast model is employed that contains both slowly varying background and vessel structures as the background model, and superimpose a deterministic signal to emulate a tumor. This study demonstrates how signal detection performance of a numerical observer will vary as a function of signal depth and imaging system characteristics. The described methodology can be employed readily to systematically optimize other OAT imaging systems for tumor detection tasks.