I generally give to the Red Cross rather than to a newer institution for relief, I like that the Red Cross is predeployed and well organised and doesn't waste a surplus.
If I were a giver to care for a smaller target group, that small group would be where I wanted the money to go, using the money otherwise is betrayal. If I were intent on general preparation or response to disaster generally I would give to the Red Cross and not more directly.
Also consider the March of Dimes , when the vaccine for Polio was developed the organisation was almost successed out of existance, they decided to take their surplus and their organisation onto a new problem. I don't mind this because the origional cause was never thereby shortchanged.