The answer can be gleaned from Big Mom’s dealing and attitude with the respective two. And let’s also view this with regards to that the theme of One Piece is, which is: deams. (Will of D)
You gotta ask yourself why Big Mom refers to Katakuri as a “lowly son”. Katakuri allegedly has an undefeated streak and his fighting prowess is unquestionable whether you believe it or not, so why talk down in that deprecating manner to her (supposedly) strongest subordinate? Because Big Mom honours strength, so that comment never made any sense at first glance.
By contrast, Jimbei commands much more respect from Big Mom. Would anyone share a different opinion on whether Big Mom respects Jimbei way more than Katakuri?
I think the reason she deals with them differently has not so much to do with power level (where Jimbei honestly is a bit stronger as he on land was equal to awakened Ace) but a lot more to do with the difference in their personal characters and values, personal integrity, dignity, and personal sovereignty. They way she respects them differently has to do with their ways of life. I
For one, Jimbei is true to his values and dreams: his life is one of his own choice and making. Jimbei is free in a way Katakuri is not.
We saw from Katakuri’s flashback that he’d rather chill back and eat donuts. That’s what he wants, to be way more ordinary and carefree. The personal sacrifices of having to be forced into a role of living up to this “invincible” figure of strength, that is one of his own making but not one of his own choice.
Also this trope of having an undefeated winning streak is certainly false. Katakuri knows this. Big Mom knows this. Katakuri is only referred to in this way as a way to bolster the morale of his own crew. Don’t get me wrong, Katakuri is certainly powerful and his being a competent Yonko commander is certainly valid (Katakuri is in my view stronger than the other Yc1). However, this trope is played up to a degree that doesn’t hold merit, simply for him to be a symbol of strength and hope, with a dual purpose to keep the fighting morale strong of his crew strong and equally to ward off enemies, both as means to protect his sibling.
Ultimately he becomes a useful idiot for Big Mom, which partly explains why she looks down on him. What Katakuri’s flashback also reveals is that this role isn’t true to his own nature. Big Mom sees that Katakuri is not true to his own nature and rhatKatakuri is not as ambitious as he seems. The flashback reveals he sacrificed his own dreams for his family, and Big Mom looks down on this weakness. Katakuri became enslaved to this ideal vision of him by others, that effectively he lost his own dream.
When you try to fit in with the world, act the way the world does and think the same way, you lose your own integrity as you’re not living your dreams. You’re living the dreams of someone else or the dreams of other people.
Katakuri effectively lives the dream of his siblings. His covering up his own face is a symbol for this act. Katakuri may have a lot of willpower, but it is very narrowly focused, to a great sacrifice and cost to his own personal sovereignty.
Jimbei is more ambitious than Katakuri and he is true to his own dreams and aspirations. Of course Big Mom respects Jimbei as she sees Katakuri as a fake, as a useful idiot for her, while Jimbei displays great personal courage, integrity and fidelity to his own dreams.
Ask yourself why Big Mom should respect Katakuri with all this in mind. Katakuri is a great representation of what you should not be. Katakuri denounced his own dream. The point of Katakuri meeting Luffy was to reconnect with his own personal dreams and aspirations.
So the question of who is the better written character might be Katakuri, but the better character is Jimbei.