These models are similar because "both the nuclear model and the solar system model have concept of nucleus, electron, positively charged nucleus at center and electrons orbiting around the nucleus".
Explanation:
The points which showcase similarities among both the atomic structure and the composition of the solar system are like the large percentage of the mass centered in the core which is the nucleus or the sun. Attractive forces bring the structure together by application of electromagnetic force or gravitational force.
The existence of the external objects influences the stable state of other surrounding objects as suggested by Pauli theory of exclusion and gravitational disturbance. Overall on the basis of the view only, in both the model their is similarity like atomic model speaks about electrons orbiting the nucleus similar to planets orbiting the sun.