The Red Cross does do some things well in the immediate wake of a disaster, but it's such a giant bureaucratic behemoth that unfortunately it's very hard to guarantee that your dollar is getting the proper leverage.
It's true that smaller orgs typically get more of your dollar directly to those affected but the tradeoff is that they typically don't have the corporate connections of a larger org. What I mean by that is that $1,000 to a local charity may enable them to purchase a pallet of water at or slightly below retail price - but a larger org will have connections with Nestle or Coca-Cola and will be able to buy 4 pallets of water for the same figure - or not pay at all. There is a term for these partnerships and the product trade called "Gifts In Kind" or "GIK." A big org will get a ton of free product from Quaker Oats and Powerade that they can then shift and distribute.
The silver lining in these differentials is that many times the larger orgs will "partner" with the smaller orgs and allow them to use their big time contacts to distribute GIK properly. That's the best synergy you can hope for because you get the efficiency and personal touch of a local charity with the corporate resources of a larger aid organization.
So, I wouldn't say NEVER give to the Red Cross but I would be cautious about it. They are great with shelters and food right after a disaster - typically.
I may have posted this before but if you want to know how an organization spends their money, go to
https://www.charitynavigator.org/ and type in the name of the company you are looking at. There are still things that can be hidden and shuffled away, but it gives you a good idea of what they are doing with most of their cash.