One difference (though I won't venture a guess for what % of the cost difference it account for) is that the U.S. has a much more drawn out and less final decision-making process. The national legislature passes very general laws, like the Clean Water Act, and charges an administrative agency with implementing them, and the courts with interpreting them and resolving disputes over what they mean. States do something similar. A city that wants to do something like build a metro line must therefore pass a series of these general requirements. They do things like prepare environmental impact statements, noise-abatement statements, seek EPA and other agencies' approval of plans, seek state approval of plans, etc. Various stakeholders or members of the general public can challenge these plans at each stage (sometimes up to a dozen or so agencies may be involved). If the plans make it through that stage, such people can then sue in state or federal court, using any of these dozens of laws, looking for an injunction to halt construction, modifications to the plans, etc. The end result of all this is a lot of delay and expense, even apart from any actual construction issues.
In many other countries the process is somewhat more legislative. A city proposes a metro line, and seeks the direct approval of higher levels of government: there are discussions, hearings, and then the plans are passed into law. Once the plan is law, then it's law: the legislature is presumed to have weighed the pros and cons and made the decision, so you can usually no longer challenge it on environmental grounds, noise-pollution grounds, or anything else, because that power is not delegated to agencies or courts.
In short: the U.S. both has a lot more layers of government (city, transit district, county, state, national), and delegates much more case-by-case decision-making power to administrative agencies and courts.
