Intuition and gut feeling helps us to attach a situation in our own way. The disadvantage of intuition is that it is not scientifically proven and it depends on one's character & experience. Most of the times, it might work and sometimes it doesn't. When it doesn't work, it becomes our learning.
Following a framework - the advantage is you can rely on it. Within the given boundary, it is supposed to produce predictable results. How the things are done is fairly fixed (it is supposed to produce almost same results irrespective of who is doing it). But the issues crop up when we do not understand the boundary (or rather underestimate the boundary). There is scope for learning by trying to improvise the framework.
Growth lies in using our intuition (new problem domain) and defining a framework to solve specific problem (that are recurrent).