OP must have facepalmed every time someone responded saying 'there's so many different types of intelligence e.g. I might be better than him at X but he might be better than me at Y' so it's impossible to compare blah blah blah.
The point is, we have an internal gauge on our intelligence level and how that compares to other people. Although grades and universities might be a tangible representation, it is more the inherent awareness of how our intelligence sits relative to others that OP is discussing.
I think that where we pitch ourselves on this invisible scale is almost like an index from many factors including but not limited to academic intelligence, social intelligence, logic and general knowledge.
Based on this, I have only met two people (both male) who I consider more intelligent than me, on my internal scale. One of them got a 2.1 at University whereas I got a 1st, which is for me reinforcement that tangible results aren't really as relevant here.
This is not me being arrogant either- I think that for me to consider someone more intelligent than I am, they have to present their thoughts and ideas to me in a way that changes my opinion or outlook, or actually teach me something. And I don't mean teach me facts. Anyone can read some information and regurgitate. It's something more than that.
p.s I'm female