The US is #1 in charitable giving because it's so easy to get a tax deduction for doing so. If people had to give out of their after-tax income I suspect you'd see a quite different picture.
That's not true. I have the experiences of having prepared taxes professionally and counting and reporting donations at a church. By combining those I can observe that the majority of donations are proportional to income, not whether the donator can fill out a Schedule A. (The ability to fill out a Schedule A and deduct donations essentially depends on whether the taxpayer has a mortgage, for middle class.)
It's not exactly a tax deduction though... In the UK, for example, charitable donations are 'tax free' effectively, since the recipient will recieve an extra amount based on the marginal income tax rate you are paying. The only beneficiary here is the charity, and only if you make an explicit donation from your after-tax income. It's not like the government is allowing you to choose to redirect the tax you're due to charity. In the US, I believe the situation is similar.
In theory a donation of $1 in the US is exactly equivalent to a donation of $.70 or so in the UK. But psychologically it seems that people are much more willing to donate more and get money from the government.
(The other thing I've wondered about is how much of the US's charitable donations are simply tax fraud).
'The taxable income of the donor is reduced by 300 USD. If the donor's income was in the 35% income tax bracket both before and after the deduction, the donor's tax liability (amount of taxes owed to the government) is reduced by 105 USD.'