The primary benefit of most deferred compensation is the deferral of tax to the date(s) at which the employee receives the income.
In the US, Internal Revenue Code section 409A regulates the treatment for federal income tax purposes of "non-qualified deferred compensation", the timing of deferral elections, and of distributions.
Although DC is not restricted to public companies, there must be a serious risk that a key employee could leave for a competitor, and deferred comp is a "sweetener" to try to entice them to stay.
A top-producing salesman for a pharmaceutical company could easily find work at a number of good competitors.
A "qualifying" deferred compensation plan is one complying with the ERISA, the Employee Retirement Income Security Act of 1974.
There is a doctrine called constructive receipt, which means an executive cannot have control of the investment choices or the option to receive the money whenever he wants.
For example: if an executive says, "With my deferred comp money, buy 1,000 shares of Microsoft stock", that is usually too specific to be allowed.
One aspect of this that has attracted both theoretical and empirical interest has been 'deferred compensation,' where workers are overpaid when old, at the cost of being underpaid when young.