Mankiw dwells on Biden's relative dislike for charity in this post.
A defense of Biden appears here. I don't buy it however. Most families I know give cash donations and contribute to society with voluntary work too, so I don't know how that could help to explain Biden's low declared charity rate.
In reality, I would expect high-income families and politically involved families to give more than the average declared share.
On the topic, it's always good to remember the wise words of P. J. O'Rourke: "There is no virtue in compulsory government charity, and there is no virtue in advocating it. A politician who portrays himself as "caring" and "sensitive" because he wants to expand the government's charitable programs is merely saying that he's willing to try to do good with other people's money. Well, who isn't? And a voter who takes pride in supporting such programs is telling us that he'll do good with his own money -- if a gun is held to his head."