The Red Cross is generally regarded as the best humanitarian aid organization out there, maybe tied with a couple others like Doctors Without Borders
I was told a long time ago that one difference between the two is that the Red Cross will only go into territories where it is legally allowed to do so, whereas Doctors Without Borders will get into conflict zones even when not welcome and risk their lives in the process. My view is we're fortunate to have both.
Note though that humanitarian aid (i.e. aid that's strictly focused on relief towards disaster zones) is generally harder and plausibly gets a lot less bang for the buck than efficiently targeted health- and development-aid. The latter also tends to get a lot less attention, which means even small-scale donors have opportunities to make a huge long-term difference if they direct their funds wisely.
The charity evaluators I'm aware of have pointed out that trying to evaluate the effectiveness of causes like disaster relief is extremely hard, despite how popular that cause is in general.
I was told a long time ago that one difference between the two is that the Red Cross will only go into territories where it is legally allowed to do so, whereas Doctors Without Borders will get into conflict zones even when not welcome and risk their lives in the process. My view is we're fortunate to have both.