Digital tomosynthesis system has been widely used in chest, dental, and breast imaging. Since the digital tomosynthesis system provides volumetric images from multiple projection data, structural noise inherent in X-ray radiograph can be reduced, and thus signal detection performance is improved. Currently, tomosynthesis system uses two data acquisition modes: step-and-shoot mode and continuous mode. Several studies have been conducted to compare the system performance of two acquisition modes with respect to spatial resolution and contrast. In this work, we focus on signal detectability in step-and-shoot mode and continuous mode. For evaluation, uniform background is considered, and eight spherical objects with diameters of 0.5, 0.8, 1, 2, 3, 5, 8, 10 mm are used as signals. Projection data with and without spherical objects are acquired in step-and-shoot mode and continuous mode, respectively, and quantum noise are added. Then, noisy projection data are reconstructed by FDK algorithm. To compare the detection performance of two acquisition modes, we calculate task signal-to-noise ratio (SNR) of channelized Hotelling observer with Laguerre-Gauss channels for each spherical object. While the task-SNR values of two acquisition modes are similar for spherical objects larger than 1 mm diameter, step-and-shoot mode yields higher detectability for small signal sizes. The main reason of this behavior is that small signal is more affected by X-ray tube motion blur than large signal. Our results indicate that it is beneficial to use step-and-shoot data acquisition mode to improve the detectability of small signals (i.e., less than 1 mm diameter) in digital tomosynthesis systems.