In the "solid" version, the contact faces are considered completely fused. If you take "no penetration", it is a contact but the relative slip between the 2 surfaces is still possible. Basically, it's like if you stack 2 sheets of paper and put glue between the 2 or not.
So, in the first case, it's as if you had a single thicker block (therefore with more inertia) and it is logical that the deflection is less important.