Different kaiju each have what amounts to their own personalities, with some being more agreeable to rear than others. My first kaiju, Sprocket, was a breeze and almost never gave me any trouble. My second kaiju was an insufferable brat that refused to perform Drills, was terrible at fighting and was extremely quick to anger. I retired that one after a few in-game months because forget that noise. My third kaiju, Crabble, was much more pleasant — though sometimes had a tendency to not do much during fights when I wasn’t in direct control.
This disparity in training experience helps to make your kaiju feel more like individuals, certainly. Though at times it can be frustrating when all you want to do is finish a Drill or complete Errantries, only to have the kaiju fail despite being old and experienced enough that it really shouldn’t be happening.
Each of your kaiju has multiple pages dedicated to various stats, traits, stills, and so on. Familiarity with their likes and dislikes definitely helps, though I can’t say it’s strictly necessary. In my experience, you don’t really lose much if you feed them something they don’t like (they might get a little mad, but you can offset that in other ways). Still, if nothing else it’s a good way to remind yourself of what they can or do specialize in, and what you can do to make them happy if they start to get a little fussy.