There aren’t many campaigns where if you say your playing a wizard your “friend” will try and one up you.
No, but you'll feel it everytime you cast a spell and the DM asks "what's your DC?" and it's one less than the other wizard in the group. It will even out if you play to the highest level, but apparently only a handful of groups do that. Even if it is not mechanically meaningful, some will feel it and it can be bothering to them (I never said it was all the people on earth, ever, just that SOME players COULD be bothered by it, without any intent to quantify their number). The "friend" doesn't need to do something to "try and one up" you, he just needs to make sensible stats assignment and be of the same class as you (which happens often with large groups).