Let's do some research:

Red Cross:

Mostly OK, but... there are some occasional issues.

https://www.charitynavigator.org/index.cfm?bay=search.summar... https://www.charitywatch.org/ratings-and-metrics/american-re... http://www.npr.org/2016/06/16/482020436/senators-report-find...

Meanwhile the Center for Disaster Philanthropy ... is smaller.

https://www.charitynavigator.org/index.cfm?bay=search.summar...

I actually can't quickly find any issues on them, though comparing the one common source they seem to have far better transparency, and lower internal overhead (I suspect more volunteers?).