A condensed version of the reason why SM is better than SSS:
Stock Market costs 10,000,000 less than SSS. To make Social Security System better, it must earn that 10million MORE than Stock Market, within 30 days.
That's right, for SSS to be better, it has to give the full bonus of SM, then 10million more on top of that. For reference, that's 333,333.33 per day roughly.
The stock market already gives you a bonus of 5.99 per citizen. So this is going to depend on your citizen count and your income.
If you have 80,000 citizens (roughly 7500 infra), you need to make an additional 4.16 per person profit from SSS to beat out Stock Market. So at 80,000 citizens, your total income boost from SSS needs to be $10.15.
I may have done the math wrong here, but using that information, I'm getting the cutoff point being 507.70 per citizen. And that's with 80,000 citizens. The lower your population is, the higher that cutoff point gets, it goes on a sliding scale.
In otherwords, unless you're buying your first wonder at 10k infra (and that makes you an idiot) SM is going to be the most efficient for you.
ps to the OP, Police HQ > Barracks.