I'm kinda in the "why not both?" camp.
Like, if someone doesn't have knowledge or practice, they're going to seem more intuitive, just because they don't have all that theory knowledge yet. Someone who has a lot of knowledge and practice and has developed a system is gonna seem more analytical, just because they have the knowledge to back up how their stuff works. Learning theory doesn't have to quash your intuition; it can strengthen it.
For example, a lot of times I'll sketch out a basic composition of a panel, and then check rule of thirds to see if it hits points of interest or not, and think about whether the composition I've drawn is good for the panel. Does that make me intuitive -- going with my gut for the initial sketch? Or does that make me analytical -- using my knowledge of composition guidelines and fundamentals to refine that sketch into a finished piece? When I check, I often find I've just hit the rule-of-thirds points naturally -- does that mean I work intuitively, or that I have a loooot of practice reworking compositions so that it's become second nature?
I think you could definitely make an argument one way or another, but ultimately I feel like it's only so useful to separate the two. It's like asking a golfer "Are you a putter or a driver?" Like, you might be better at one or the other, but you're probably going to practice and use a mix a both.