it depends on the solvent
for example dimethyl sulphoxide would be polar enough to dissolve the ionic compound ,it is not protic ,therefore for OH- and SH- , a large percentage of the product would be Substitution products as the nucleophilicity of the chemical species would not be suppressed
however if use a polar protic solvent like water, the nucleophilicity of the chemical species OH- and SH- would be suppressed, therefore a majority of the products would be elimination products
If assuming the chemical species OH- and SH- are used in the same solvent,SH- would be a comparatively stronger conjugate base of H2S as compared to OH- as a conjugate base of water,this is because as oxygen is more electro-ve than sulphur , the dipole moment btw sulphur and hydrogen would be much smaller than the dipole moment btw oxygen and hydrogen, hence this would cause the -ve charge on S to be less than the -ve charge on O
Therefore,as SH- is more stable than Oh- , the eqm lies more to the right , hence less likely to act as the base, therefore there would be greater % of SN products as compared to the % of substitution products of OH-
hope u will understand my explanation