I previously stated in the comments:
Both are just as wrong or as right as the Lewis structure of thionyl chloride.
Indeed thionyl chloride is a nasty little molecule when it comes to the bonding situation. This makes it also incredibly difficult to utilise it in quantum chemical calculations. I have tried to answer a similar question, but eventually gave up due to the complexity of all the involved species.
However, I would like to share a few insights, that might make the whole problem at hand a little bit more comprehensible.
Let us start with the bonding situation in thionyl chloride and its structure. The representation you have used cannot be completely right. As it is drawn, it omits the lone pair at sulfur, implies instead a double bond, and hence suggests that sulfur is trigonal planar coordinated. This is not true.
If one would want to chose a single representation of this molecule it should be a charge separated one, preferably one that indicates the pyramidal structure. A more accurate representation would be as a resonance hybrid. I have performed a calculation on the DF-BP86/def2-SVP level of theory, which I analysed with the Natural Resonance Theory (NRT) of the Natural Bond Orbital (NBO) theory.
What we can already assume from the picture is that the sulfur chloride bonds have significant ionic contribution. This manifests when we look further into the analysis. I include a short version of the analysis, skipping over the core orbitals and truncating minor contributions from polarisation functions. The following is for the major contributor of the bonding situation.
# (Occupancy) Bond orbital / Coefficients / Hybrids
------------------ Lewis ------------------------------------------------------
17. (1.99836) LP ( 1) S 1 s( 77.03%)p 0.30( 22.93%)d 0.00( 0.03%)
18. (1.99504) LP ( 1) O 2 s( 75.06%)p 0.33( 24.93%)d 0.00( 0.01%)
19. (1.67421) LP ( 2) O 2 s( 2.02%)p48.34( 97.83%)d 0.07( 0.15%)
20. (1.64705) LP ( 3) O 2 s( 0.00%)p 1.00( 99.85%)d 0.00( 0.15%)
21. (1.99928) LP ( 1)Cl 3 s( 92.72%)p 0.08( 7.28%)d 0.00( 0.00%)
22. (1.95239) LP ( 2)Cl 3 s( 1.12%)p88.55( 98.84%)d 0.04( 0.05%)
23. (1.93382) LP ( 3)Cl 3 s( 0.32%)p99.99( 99.63%)d 0.15( 0.05%)
24. (1.99928) LP ( 1)Cl 4 s( 92.71%)p 0.08( 7.28%)d 0.00( 0.00%)
25. (1.95238) LP ( 2)Cl 4 s( 1.11%)p88.67( 98.84%)d 0.04( 0.05%)
26. (1.93381) LP ( 3)Cl 4 s( 0.32%)p99.99( 99.63%)d 0.15( 0.05%)
27. (1.99082) BD ( 1) S 1- O 2
( 34.00%) 0.5831* S 1 s( 16.81%)p 4.88( 82.01%)d 0.07( 1.18%)
( 66.00%) 0.8124* O 2 s( 23.03%)p 3.33( 76.66%)d 0.01( 0.31%)
28. (1.99354) BD ( 1) S 1-Cl 3
( 41.14%) 0.6414* S 1 s( 3.74%)p25.50( 95.33%)d 0.25( 0.93%)
( 58.86%) 0.7672*Cl 3 s( 5.84%)p16.06( 93.78%)d 0.06( 0.38%)
29. (1.99355) BD ( 1) S 1-Cl 4
( 41.14%) 0.6414* S 1 s( 3.74%)p25.49( 95.33%)d 0.25( 0.93%)
( 58.86%) 0.7672*Cl 4 s( 5.84%)p16.06( 93.78%)d 0.06( 0.38%)
---------------- non-Lewis ----------------------------------------------------
30. (0.07913) BD*( 1) S 1- O 2
( 66.00%) 0.8124* S 1 s( 16.81%)p 4.88( 82.01%)d 0.07( 1.18%)
( 34.00%) -0.5831* O 2 s( 23.03%)p 3.33( 76.66%)d 0.01( 0.31%)
31. (0.36862) BD*( 1) S 1-Cl 3
( 58.86%) 0.7672* S 1 s( 3.74%)p25.50( 95.33%)d 0.25( 0.93%)
( 41.14%) -0.6414*Cl 3 s( 5.84%)p16.06( 93.78%)d 0.06( 0.38%)
32. (0.36856) BD*( 1) S 1-Cl 4
( 58.86%) 0.7672* S 1 s( 3.74%)p25.49( 95.33%)d 0.25( 0.93%)
( 41.14%) -0.6414*Cl 4 s( 5.84%)p16.06( 93.78%)d 0.06( 0.38%)
What we learn from this is that all bonds are polarised away from the sulfur, giving the compound significant ionic character. The lone pairs of the oxygen atom are not fully occupied. This will be a bit clearer, once we look at the canonical orbitals. Also very interesting is the fact, that the anti-bonding orbitals (labelled BD*) of the sulfur chloride bonds have non-negligible occupations. This is essentially the electron density missing from the lone pairs of oxygen.
The above table can be nicely put into a picture. You might have to click and enlarge it. The contour value is set to 0.05 a.u. and we still see how massive the lone pair at sulfur is (occupied blue/orange). We can imagine that this electron density effectively could shield a nucleophilic attack at one of the virtual orbitals (red/yellow).
We can further verify the predominantly ionic nature of the bonds by looking at an analysis in terms of the quantum theory of atoms in molecules (QTAIM). Here we can look at the electron density at the bond critical point to compaer their relative strengths and at the value of the Laplacian at that point. If it is positive, then we know it is an area of charge depletion, if it is negative we know that it is an area of charge accumulation. The former we associate with a predominantly ionic nature, while the latter would be found in more covalent compounds. For the three bonds we find the following on the same level of theory as above. The analysis was done with MultiWFN. (Critical points 1-4 are the nuclei.)
#CP Atoms El. Density Laplacian
----------------------------------------
5 S-Cl 0.106 0.086
6 S-Cl 0.106 0.086
7 S-O 0.263 1.251
This nicely agrees with our previous assignments.
Now it's time we look at the canonical orbitals. These are the orbitals wie initially obtain from a calculation. The NBO analysis then transforms them into localised orbitals, which are easier to interpret. Of course this approach destroys the symmetry of such orbitals. For that we have to look a the delocalised pictures.
More specifically, we do not see any contribution of π bonds to the bonding picture. The following picture contains the occupied molecular orbitals starting at number 17 (omitting non-valence orbitals) in the top left corner to the HOMO (No 29) in blue/orange. The last line contains the LUMO (30) and the two orbitals above it (red/yellow).
The first orbital (17) we see, nicely represents the sulfur oxygen σ bond. The next two orbitals give partial bonding to the sulfur chlorine bonds. The fifth orbital is an in-plane π orbital of the sulfur oxygen bond. The seventh orbital can be seen as the out-of-plane π orbital. All other orbitals correspond to linear combinations of lone pairs. What we learn here primarily is that those orbitals do not really have the interpretative value we wish they would have.
The LUMO corresponds the an anti-bonding contribution to the out-of-plane π bond of sulfur and oxygen. This is the orbital where the nucleophilic attack would happen. The LUMO+1 corresponds to the anti-bonding in-plane π orbital and to the anti-bonding configuration of the chlorine sulfur bonds. The LUMO+3 is already the anti-bonding σ sulfur oxygen bond.
From these pictures is seems very likely that a concerted mechanism, direct displacement of chlorine, like the one in your left picture, can not occur.
Your second option is basically already ruled out, since we do not have a π bond of appropriate symmetry.
This leaves the option of addition elimination, a two step mechanism. Or does it?
Well as initially stated calculations of the mechanism, respectively the whole system are incredibly difficult to perform, and even if they would lead to results, I would take with a grain of salt. However, there is a bit evidence, that a tetra-coordinated species could be stable. At least at the DF-BP86/def2-SVP it is a minimum on the potential energy surface. I chose bromine as a nucleophile, because it is fairly simple. This is obviously nowhere near conclusive, it is just a tiny piece in the complete puzzle.
And for final thoughts on the matter I performed a parameter scan of first the bromine sulfur bond and then the sulfur chlorine bond. It appears that on this level of theory the association is barrierless. (Please note that the y-axis has not the same scaling in the graphs.)
But there should always be an alternative thought on the matter. Considering the large ionic contribution of the bonds, one could also assume a dissociation association mechanism, hence creating a strong electrophile, which can possibly be attacked by any nucleophile (even weak ones). The whole process is dependent on many features.
$$\ce{OSCl2 <=>C[-Cl-] [OSCl]+ <=>C[+Nu- ] OSClNu}$$
I was unable to find any literature beyond the phenomenological explanation given in most organic chemistry textbooks. The mechanism of these kind of reactions may remain somewhat of a myth - or an educated guess. Any kind of mechanism that only implies transition states, i.e. electron-pushing or arrow mechanisms, are descriptive at best. Whenever we invoke Lewis structures - even though it works in more than 90% of the times in organic chemistry - we have to question the overall validity of that approach. Lewis structures are easy to understand, but have serious limitations.
