I don’t think of EL DORADO as a remake of RIO BRAVO, I think of them as variations on a theme. (Way less successful was RIO LOBO, which reversed the roles: the bad guy is the sheriff holding one of Wayne’s friends hostage, and Wayne and company are the ones trying to break into the jail.)
But sticking to the first two: I think RIO BRAVO is a great film, totally likeable, and we watch it at least once a year just to enjoy. EL DORADO has more pain than RIO BRAVO, and more violence. There’s more emphasis on mortality, on aging, and on physical deterioration that comes with age. If you look at the scenes that are different (in EL but not in RIO), I think you’ll see that. The boy’s suicide, for example, has no parallel in RIO BRAVO; shot in the stomach, he kills himself because he can’t bear the pain. Similarly, Wayne’s physical disability (caused by a bullet against his spine) isn’t found in RIO BRAVO: he clutches his side after every physical activity; he collapses twice, totally helpless, partly paralyzed.
The level of pain and violence is much higher: For compare/contrast, consider the scene where Wayne hits a lying bad guy in the face with a gun – the violence level and pain in EL DORADO is way more extreme, it’s not just a whollop (with a rifle, not a gun), it’s a clearly supressed desire to kill. The bit where Wayne forces a gunman out through a door to face an ambush by shooting him in the shoulder and leg, has nothing comparable in RIO BRAVO.
Mitchum’s alcoholism is seen primarily as physical, where Dean Martin’s was psychological/spiritual. The cure for Mitchum’s alcoholism is a physical remedy (James Caan’s disgusting concoction) compared to the (much more realistic) self-will and spiritual growth for Dean Martin faces.
One mild clue: When Wayne first meets Maudie (Charlene Holt), she says that he helped her when her gambler-husband was killed: that was the story of Feathers (Angie Dickinson) in RIO BRAVO. I read that as saying that EL DORADO is basically RIO BRAVO ten years later, with the characters older and mortality more imminent.
One more point: at the end of EL DORADO, both Wayne and Mitchum are on crutches. Yes, it’s funny, but there’s a dark undertone to EL DORADO that’s absent in RIO BRAVO. I’m not saying it’s a dark film – to the contrary, the dark is well hidden under the action and humor. But it’s there, for sure.
It can be argued that this is just the trend in movies, towards more violence, but I don’t think that’s a sufficient explanation.