I presume that "data" was a typo and you meant "kata".
I can't speak for Modern Arnis, but BJJ does not have kata.
Most BJJ gyms do not require memorization as such. The expectation for promotion is generally that you have functional skills in the various positions that you might end up in. So the teacher would generally look at things like how good you are at passing guard, escaping mount, finishing submissions from side control, etc in sparring.
A small minority of schools have some sort of standardized curriculum that you need to be able to demonstrate during belt tests (specific escapes from a headlock or a bear hug, for example), but not a set sequence of solo moves that you have to memorize like a Karate kata or a TKD poomsae.