Substitution at thionyl chloride sulfur
Your second drawing would imply a $\ce{S=O}$ double bond, due to available orbitals it would be a d-p &#x3c0; bond. There is considerable debate as to whether these bonds even exist with most of the evidence presented here at chemistry.stackexchange.com pointing towards a ‘no’. That would rule out your second mechanism.

That said, your first mechanism suffers from comparing sulphur with carbon too much. You assume a rather short-lived transition state and direct displacement. I don’t know for sure, but I don’t think that is the case.

Rather, I would propose a two-step mechanism with a medium-lived tetravalent sulphur. In this mechanism, the attack of the nucleophile would turn pseudotetrahedral (one corner of the tetrahedron being a lone pair) into a pseudo-trigonal bipyramid or a see-saw with $\ce{Nu}$ and $\ce{Cl}$ forming a four-electron-three-centre bond. This would then collapse back into a pseudotetrahedral product liberating the better stabilised anion. Close to your first mechanism, but not identical: