If you have a set budget for staffing a project, is it more productive to give lower wages with a bonus structure or to pay higher wages to all staff?

Bonuses usually work better, for two reasons:

- Bonus is an incentive pay beyond expectation, it will work as motivational tool

- Unlike high salaries (in other words, base pay increase), bonus is not an additional permenant cost to your payroll budget. Moreover, any increase in base pay will drag other cost like increase in other allowances, or higher "end of services" benefits,  

I agree with Mr. Khaled opinion, But also i would like to add, Based on Nature of work and industry

Both can work , but it depends on the kind of stuff you`re dealing with ( Seniors , Mid Level or starters).

From my opinion   bonuses are very important specially when it comes to project staffing.

Once they finish their project on time with no mistakes in a professional way they do deserve the bonus. They`ll be soo motivated and fresh getting ready to handle their new project , while monthly high wages can cause lack of concentration.