If we are going to look at the difference between theists and atheists with respect to charitable giving, one of the concepts we should introduce is that of rational charity. This is the idea of putting one's money where it can do the most good, and not wasting money on that which has no effect, or that which actually harms the people that one is trying to help.
We get significant examples of this from religious charities.
There are those who devote a considerable amount of effort building churches where they could be building water treatment plants, and teaching a set of religious myths where they could be teaching people to better understand the real world in which they live.
They do more harm than good by teaching that which substantially ignorant tribesmen who have long been dead once held to be immoral as if those ignorant tribesmen had perfect knowledge. They encourage behavior that is destructive, discourage behavior that would be helpful, and institutes an attitude that any who would dare to question these ancient and false beliefs must be condemned as heretics.
However, even if one gets around these problems, there is a great deal that one needs to know in order to engage in rational charity. There is so much information out there that most of us base our decisions on very little information. In fact, we are more likely to be guided to make our decisions based on proximity than on reason - those organizations that are closest to us and easier to reach as opposed to those that do the most good.
We have ways of knowing the types of things that are relevant to determining how much good can be done by a particular set of actions Mostly they involve the types of research that scientists are particularly good at conducting. You take a course of action, you compare it to relevantly similar actions, you look at the various outcomes, and you pursue the option that produces the best outcomes.
It takes a lot of work to determine whether your charitable dollars are being used properly. However, the work could well be worth it. $250 worth of effort that goes into seeing that a $750 contribution will be well spent is better than a $1000 contribution to an organization that wastes $500 on activities having no effect, or spends $300 doing $700 of harm while spending $700 to do only $500 in good.
This is a risk that one takes when one's charity is directed by the recommendations of substantially ignorant tribesmen who have been dead for centuries written into some ancient book.
If each of us has to do that work ourselves it would take a great deal of effort - and it would be wasted effort. It would be more rational to assign the task of selecting charities to somebody we can trust, who will then do the effort of determining the quality of the plans created by the recipients of that money.
Those trusted individuals could then give us the results of their research, helping the rest of us to ensure that our charitable contributions go to organizations that do more good and less harm with the resources we give them.
In fact, it may be worthwhile to pay such an organization to research these types of issues and get back to us. A $1000 contribution to an organization that takes $100 off the top to make sure that the remaining $900 goes to where it will do the most good is far more efficient than $1000 to an organization that pursues some type of magical solution to a real-world problem or one whose philosophy has its members performing or advocating behavior that is actually harmful.
The best method for determining whether a charity is doing a good job is to employ the tools of verifiable premises and logical reasoning that have been such a benefit to science generally. The fact that the leaders of an organization are pious is not sufficient to conclude that they are doing a good job. One should look instead at what the organization has actually accomplished with its money in the past, and at the quality of reasoning used in determining what actions will produce the best outcome going forward.
Do the leaders of the organization respect the principles of reason and evidence when it comes to making plans?
The consequence of this approach should be the ability to do more good with the resources that are available - save more lives, put more families on a more secure foundation, promote more effective forms of education, provide education in those areas that are the most useful, promote rational economic and social reforms, and the like.