Topological perception theory (TPET) explains perception with geometrical properties，as well as emphasizes the priority of topological perception which is the basis other geometrical perception depends on. Topological perception also occurs first among all of the geometrical perceptions. When target is presented for only 5ms, difference among topological properties could be distinguished. Visual system firstly perceives topological properties, secondly projective properties, thirdly affine properties, and finally Euclidean properties. As for topological primacy theory(TPRT) ，it claims the developmental sequence of children's space conception is topological, projective and Euclidean. Before 4 years old, children’s space conception is topological, and they don’t have shape and size constancy ( shape and size are Euclidean properties ). Although both of the two theories explains psychological phenomena by topological, there are some differences in their objects and methods. We will compare these two theories in research contents, methods and theoretical structures. In research contents, there are three main comparisons. Firstly, in geometrical properties, both of the two theories research topological, projective and Euclidean properties; otherwise, TPET researches affine properties. They define geometrical properties in different ways. Secondly, the psychological phenomena they’ve researched are different——TPRT researches space conception, emphasizes mental representation of space instead of perception, while TPET researches visual phenomena, such as apparent motion, illusory conjunctions and global precedence, Although the two theories are different in objects and methods, their theoretical structures are highly consistent. Last but not least, participates are different——TPRT researches children, while TPET researches adults and animals, which enlightens geometry utilizing on psychology. Comparatively speaking, methods of TPET are more objective and rigorous, and have higher reliability and internal validity, for other researchers have found the same results with TPET when used the same methods; as experimental scenes of TPRT are similar with real life, results of TPRT have higher external validity. However, irrelevant factors are not controlled strictly which leads to lower internal validity. These two theories have similar theoretical structures. The theoretical structures are in line with stability of geometric properties——topological properties are most stable, projective properties are less stable than topological properties and more stable than affine properties, and Euclidean properties are the most unstable.