Europeans prefer the state to help needy causes, Americans have a preference for charities to take care of this. Are government support and philanthropy substitutes or complements? If they are perfect substitutes, then it would not matter what the source is. If they are complements, you would want both to be in play.
James Andreoni and Abigail Payne point out that there is more to the story than simple crowding out. Suppose that a government provides some resources to an organization, say $100. Then people will contribute $56 less. But not all this crowding out is coming from people feeling they are not needed any more. $38 of this $56 reduction are due to lower fund raising effort. This makes it particularly important that any money the government gives should have a matching requirement from private funds to maintain the fund raising effort.