I know that God is not popular on Slashdot, but even from a rational humanist perspective these charities are very effective. The administrative costs are usually born by regular tithing so any funds given to the charity can be spent 100% on the core mission of the charity. Especially, in the area of disaster relief, these charities also have strong connections with the local congregations who can quickly put resources to use where it is most needed. This in contrast to groups like the Red Cross usually have to spend time "getting in" to places.
I know there will be some objections voiced that the money will be used to evangelize victims rather then aid them. I cannot speak for other sectors of the religious sphere, but charities associated with Mainline Protestant Christian churches operate in perpetual fear of this accusation and copiously avoid any activity that might be mistaken for proselytizing.
I will end by plugging the charity of my own Episcopal Church: Episcopal Relief and Development.