Yeah, 的 attaches to different things and expresses a different nuance, but it’s hard to express it with a definition.
You have stuff like 経済 (economy, finance) and then 経済的 (economic, financial)
比較 (comparison) 比較的 (comparative[ly])
世界 (world) 世界的 (worldwide, global)
EDIT: Okay, looking up monolingual definitions, it’s basically… with みたい and よう, you are taking a thing and speaking figuratively that it is like another thing, whereas with 的, you are distilling the thing it attaches to down to a quality.
I can find examples of people using 猫的, but it’s not interchangeable with みたい in those situations.
It’s true that -like in English overlaps with both uses though.
It feels like, the more you are talking about something observable and concrete, 的 feels wrong, but I was able to think of a place where they probably are both possible, with different nuances.
猫みたいな反射 - cat-like reaction (in physical appearance)
猫的な反射 - cat-like reaction (just in the quality of speed or precision)
Both could be used in some situations, but the framework is different. (And note that just because I can imagine these two doesn’t mean they are actually natural or would be used by natives)