I agree in general on reducing the number of federal employees, but the comparison given above is not apples-to-apples.

The metric used above is intended to inflame, rather than inform.

The private employment number include all employees, including fast food workers, retail, construciton laborers, etc.
The federal government employees skew towards higher educated positions. The equivalent of the above private jobs (cafeteria work, construciton labor, retail) are contracted out to the private sector by the federal government.

In fact, as we reduce federal employment to fewer numbers, the approach has been to keep the oversight and management government positions, and outsource the lower-paid positions.
So, as we right-size the government, this metric will probably continue to skew higher for the average federal employee, compared to average private employee.

A better metric would be a comparison of wages and benefits for similar positions at various levels. If one looks at that comparison I would suspect that the higher end jobs (engineering, management) pay signficantly more in salary/benefits in the private sector than in Federal employment, while lower end jobs likely pay more in the federal govt than in privsate employment.