I would take that bet. First, government office workers have a higher bar to entry. While I've heard criticism of them being myopic, it was rarely that they were lacking intelligence.

Deloitte consultants have a much wider variance. They too are capped on how much they can be paid, but they do not get the benefits of government service (e.g. pensions.) They are shuffled from subcontractor to subcontractor and the project managers are more obsessed with extracting more money from the department than finishing the project. The incentives are so misaligned as to be comical.