When the S corp wins
As a sole proprietor or default LLC, self-employment tax applies to 92.35% of everything you clear: 12.4% for Social Security up to the annual wage base and 2.9% for Medicare on all of it. As an S corp, that same 15.3% applies only to the salary you pay yourself. Whatever is left is a distribution, and distributions do not pay it.
The saving is 15.3% of the gap between your profit and your salary. At $150,000 of profit with a $60,000 salary that gap is $90,000, so the payroll-tax saving is roughly $13,000 before costs. At $60,000 of profit with a $40,000 salary the gap is $20,000 and the saving is about $3,000, which the costs below eat. That is why the answer is a threshold, not a yes.
The savings at every profit band, with the formula →