S vs O as a Neighbouring Group

In a first order analysis, a nucleophilic/electrohilic interaction can be approximated by the interaction of two key molecular orbitals; the HOMO (the nucleophile) donating a a pair of electrons to the empty LUMO (the electrophile). This interaction depends on: These two effects can be probed by a molecular orbital calculation on the two reactants, for which acetolysis for the S system shown below is observed to be 109 faster than for the O analogue.

The results (ab initio 3-21G* level) are as follows.

The difference amounts to 157 kJ (1 Hartree = 2624 kJ). The spatial overlap can be seen below. On both counts, S wins over O.
S bicyclic O bicyclic

Product Stability

One can test the above (reactant based) conclusions by calculating the energy of the carbocation resulting from elimination of Cl-.
Thus the energy to create a cation from the O system is +980 kJ whereas that for the S system is +898 kJ (AM1 calculations). Solvation and other factors not withstanding, this difference of 82 kJ abundantly explains the difference in solvation rates. Notice in particular that ring strain prevents the O system from closing to form an oxonium ion, whereas the larger more flexible S system does indeed so close.