how does the government use cost-benefit analysis to evaluate competing projects?

First it looks to see if Women are running it. If they are that ends the analysis. Affirmative Action.
Second, is a <minority> running it. If they are that ends the analysis. Affirmative Action.
Third, does a member of congress profit from it. If they are that ends the analysis.
Otherwise it will depend on who underestimated the costs more.

They use economic cost and benefit, not an accounting one. It means with all opportunity cost you can get. The best cost-benefit project will be chosen. But until these days, they have to carry out extra environmental study too.

Cost-benefit analysis is one of the most simplistic means of determining the feasibility of a project. The costs of the project have to be smaller than the benefits associated with it. Combine this with crucial difference analysis, and determining the legal, social, political, and ethical ramifications of the various projects and you can determine which project is the best among all the alternatives.