Tax incentives impact how much people give to charity, and are stronger among high income people. One of the most thorough empirical studies of the matter estimates quantitatively the sensitivity of charitable giving to tax incentives in the the past several decades.
The researchers estimate (as I read it based on a quick read of the article) that a long term 10% increase in the after tax cost of making a charitable gift with reduce charitable giving by about 7%. A temporary 10% increase in the after tax cost of making a charitable gift, counterintuitively, reduces charitable giving only about 5%.
Lower overall taxes have mixed effects. On one hand, lower marginal tax rates increase the after tax cost of making a tax deductible charitable gift. On the other hand, lower marginal tax rates increase income which tends to increase charitable giving by a portion of the income gain. A permanent 10% increase in anticipated lifetime after tax income tends to increase charitable giving by about 9%.
The research generally supports the notion of the "permanent income hypothesis" which is that people are more responsible to anticipated changes in their lifetime income than they are to their short term incomes. For example, students generally live above their current means because they anticipate earning more when they graduate, and people who perceive themselves as being temporarily underemployed spend more than those who perceive themselves as currently being fully employed.
The study focused on the impact of income taxes, and thus, it is hard to determine how applicable it is to the impact of the estate tax on charitable bequests.