Would it be wrong of me to be upset if my best friend applied at the same job?
Well, it depends on why you don't want him to apply?
I don't want him to know that I'm the best candidate because he'll be quicker than me.
It's wrong to tell your friend they can't apply. They have every right to apply for whatever job they want.
But he will.
That's just something that you will have to deal with, because if he is truly your best friend then you shouldn't try to kill his ambition or ruin his goals. How would you feel if he tried to stop you from getting a job that you really wanted?