Actually, this is pretty normal for that age. My son and his best friend went through something similar in K. It has to do with them always being together. Live next door. Ride the bus together. Same class. They were together 7h a day, and then afterschool too! ...Stuff like .. 'I got an A and you only got a B'. I can read at a 2nd grade level and you can't. He even went so far as to say in front of me that his dad was smarter then my husband because he just got a job making x dollars and hour and 'your dad doesn't make that much.' He was so proud. I bit my tongue hard to not burst his bubble and tell him that I make more than that.... :-)
Anyway, what helped in our situation was limiting the amount of after school time that they are together. I also requested, and the teacher agreed that they be in different classes for 1st grade.
The friend and his family are just the kind of people that feel they always have to be right and have the last word. His mom does it to me and my mom also. Its just the way they are.
We still have problems with the competition, but I finally got my son to understand that there are somethings that my son is better at, and some that the friend is better at. Like just last week, my son not only finished a test on time (yeah!!! The teacher and I were shocked!!! ), but was the only one to get all of the answers correct. Even over his friend.