In recent years, the problem of acquiring omnidirectional stereoscopic imagery of dynamic scenes has gained commercial interest, and consequently, new techniques have been proposed to address this problem. The goal of many of these new panoramic methods is to provide practical solutions for acquiring real-time omnidirectional stereoscopic imagery for human viewing. However, there are problems related to mosaicking partially overlapped stereoscopic snapshots of the scene that need to be addressed. Among these issues are the conditions to provide a consistent depth illusion over the whole scene and the appearance of undesired vertical disparities. We develop an acquisition model capable of describing a variety of omnistereoscopic imaging systems and suitable to study the design constraints of these systems. Based on this acquisition model, we compare different acquisition approaches based on mosaicking partial stereoscopic views of the scene in terms of their depth continuity constraints and the appearance of vertical disparities. This work complements and extends our previous work in omnistereoscopic imaging systems by proposing a mathematical framework to contrast different acquisition strategies to create stereoscopic panoramas using a small number of stereoscopic images.