I don't know if anyone has made a serious attempt to tackle that question, but I would also be surprised if many people genuinely believe that donating a dollar to the US federal government is better for society than donating it to any remotely competent charity.

If you're donating to specific government programs, sure, some of those are pretty similar to charities (although you can probably find a more efficient charity in nearly any area of focus). But simply donating a dollar into the funding of the US government, and having it split the same way that all US government revenue gets spent, seems to me like an obviously poor choice.