Intuition is one's instinctive sensitivity and awareness.
Intellect is one's mental capability to understand.
Intelligence is one's ability to decipher, distinguish and differentiate.
Insight is what one comprehends from one's perceptions.
Given these distinctions, it would seem that intelligence and insight serve one more than the other two.
While intuition and intellect are valuable and even admirable attributes - intelligence and insight are how we express and apply what we experience, know and understand.