109.5 vs 120?
Those are the ideal angles.
But with a caged or bicyclic compound, the angles are locked in. So your starting compound and your carbocation intermediate will have approx. the same angles.
Before you some sp3 hybridized carbons with bond angles of < 109 degrees. Afterwards we have an sp2 hybridized carbon with bond angles that are still less than 109 degrees. Meaning, the sn1 route will increase the amount of angle strain on the molecule.
That is my line of thinking on this problem.