I think it has to do with the fact that more people in the US reject public welfare systems and instead endorse private donations on a Christian religious basis, and that European countries were secularized earlier than the US (which currently undergoes a massive and rapid secularization, though). I haven't looked for any data, so take this with a grain of salt, but I'd bet that more people in Europe than in the US accept that the state should help people in need and has an obligation to secure basic welfare of all citizens. I also believe that people in the US are generally willing to pay less taxes than people in Europe, at least it seems like that judging from their voting behaviour.

If private donations are more entrenched in a society for religious reasons, then this will likely also influence people who have no religious motives.

Another explanation would be that the gap between rich and poor is larger in the US than in Europe, and so rich people in the US have a worse conscience than rich people in Europe (who often turn out to be much richer than they think they are and also show it less on average).