It is hit or miss as to if given two identical jobs, the federal job pays more or less than the private sector job. However, in many cases, the private sector employee works more hours to get the higher pay. Even GS-15s have to "punch a clock" and are limited to working a maximum of 40 hours a week. Go find someone in charge of hundreds or perhaps a thousand people in the private sector and ask them if they work only 40 hours a week. Also, in the federal sector, anyone who is a high-level manager has a deputy in their structure. The days of vice presidents in the private sector having assistant vice presidents or managers in the private sector having assistant managers are long gone. Even dedicated administrators are long gone for many.
Super competent, motivated, federal employees are a rarity, because federal employees meeting those criteria are often recruited away to work higher potential jobs in the private sector.
People who desire safety and job security over personal ambition and financial success stay in the federal sector.
The only way to get private sector efficiencies in the public sector is to get rid of the white-collar public unions, and go to a pay for performance model.
In reality the Fair Labor Standards Act doesn't apply to federal government employees, but it does apply to their equivalents in management and support at USPS. In reality the agencies make management and support personnel work under conditions approximating those that would apply if FLSA applied.
Here's where all the funny stories about government management come from ~ SCHEDULE C and APPOINTEES. That's where you get your pukes who never show up or spend all day in the toilet.