Honestly there is nothing wrong with the way either of them are written, but the biggest glaring issue with Kaido is that there hasn't been enough focus on him. With Big Mom, her actions or lack thereof became justified after her flashback. She has the mentality of a child, but the strength of an absolute monster. So all the gaglike moments that pertain to her character can be excused, because she was never meant to be the most competent person to begin with. She has a one track mind, and when she wants something, she goes for it, as a child would. She loses focus around her on anything that doesn't pertain to the immediate thing she is currently fixated on.
With Kaido, there is no context to his behavior. The most we know about him is that he values strength above all and has a tendency to "try to commit suicide", but we don't know why. None of his actions or lack thereof are justified because we don't fully know what makes him tick. We have bits and pieces of information that we can try to put together, but we need to know the full story. Yeah, he's a Yonko and commands a powerful crew, but at the same time, Oda typically focuses on Kaido as an individual with the information we are given. It's always "He alone" when it comes to Kaido. His strength alone is what got him recognized as a Yonko. He alone challenged the World Government and other Yonko's.
To me it seems like even though Kaido is a Captain of a Yonko crew, it's mainly just a facade, and he doesn't really care about it, because he can't get what other Pirate crews have. He forces people to submit to him and be "apart of his crew" using his overwhelming strength, but it lacks the comradery of a typical crew. He's trying to achieve what other crews have, but his means of going about it is all wrong. Most pirate Captains are respected by their crew, so there is a certain dynamic between everyone. In the case of the Beast Pirates it seems they are held together through fear of Kaido over anything else. He breaks their will, and forces them to submit to him. I don't think this is what Kaido actually wants, but it's the only way he can achieve what others have that he wants.
This is just my take on him from the tiny little clues we have to go on, but I fully expect that Oda will be giving him his own flashback that will flesh out his character and put everything into better perspective.