I've started to consider intuition and intellect to be the same force, distinguished by speed and perhaps by how it is accessed.
When intuition manifests itself, it usually seems directed by a part of my brain that does not fall under my ego-program. It has to be injected into the Wild World before I'm cognizant of it. But, once I am, my thinking process can get to work on either it or its corollaries, before I shelve it for the time being. Then, sometime later, it will re-enter the conscious world with those enhancements packaged together by further development in the ego-less realm.
Perhaps the ego-realm is supposed to deal with problems like "Make tool, dig hole" whereas the intuition "force-process" can work underneath this without distracting. Then when the ego-realm is confronted with another situation, the intuition can suggest a method to do the action the ego-realm wants to commit.
I would consider both to be a type of thought and I don't see how one is really possible without the other. Intuition does seem superior in the sense that its conclusions aren't directly effected by ego, but it needs something to trigger it - and occasionally, to check it.
I occasionally reach states where both seem to be happening simultaneously - i'll think on a topic, something connected will enter my mind, the first will vanish, then I'll move on from the second and something combing both will enter my mind, ad nauseam.
The problem is I'm not doing anything else productive during these states. I tend to pace. Socrates stared at the sky. crows probably fly.