The main issue with mixins is that the origin of behavior becomes opaque. If I call this.mixinFunction(), it's not defined in my file or imported directly, so I have to know exactly which functions come from which mixins. With higher-order components, you can just look at the props and know where things originated.
I'm not a staunch defender of any particular approach, but I think that's the main argument against mixins. (And it applies to other languages as well, such as Ruby.)