Fish Tank Virtual Reality (FTVR) displays create a compelling 3D spatial effect by rendering to the perspective of the viewer with head-tracking. Combining FTVR with a spherical display enhances the 3D experience with unique properties of the spherical screen such as the enclosing shape, consistent curved surface, and borderless views from all angles around the display. The ability to generate a strong 3D effect on a spherical display with head-tracked rendering is promising for increasing user's performance in 3D tasks. An unanswered question is whether these natural affordances of spherical FTVR displays can improve spatial perception in comparison to traditional flat FTVR displays. To investigate this question, we conducted an experiment to see whether users can perceive the depth and size of virtual objects better on a spherical FTVR display compared to a flat FTVR display on two tasks. Using the spherical display, we found significantly that users had 1cm depth accuracy compared to 6.5cm accuracy using the flat display on a depth-ranking task. Likewise, their performance on a size-matching task was also significantly better with the size error of 2.3mm on the spherical display compared to 3.1mm on the flat display. Furthermore, the perception of size-constancy is stronger on the spherical display than the flat display. This study indicates that the natural affordances provided by the spherical form factor improve depth and size perception in 3D compared to a flat display. We believe that spherical FTVR displays have potential as a 3D virtual environment to provide better task performance for various 3D applications such as 3D designs, scientific visualizations, and virtual surgery.