Where a one-upper tells you a bigger and better story, usually by making it up, a Legitimate One-Upper doesn't make anything up because they really are bigger and better than you.
Player: Dude, you see those girls over there? Yeah. I totally banged them last night..
Rich Player: Oh them? I did them last weekend. And their sisters...
Player: *Mutters* Damn, you Legitimate One-Upper...