There will always be an undercurrent of competition and combativeness between you, but it could be more than just a feeling. Something about your friend's personality will rub you the wrong way, and elicit passionate reactions from you that may surprise even you. And you'll rub them the wrong way, too; your drives and ambitions will seem off-target to them, and you can bet you'll have more than a few disagreements about your goals and how you move toward them.
Needless to say, these frustrations could easily mount and spell the end of the friendship, but it doesn't have to be that way. This connection could, in fact, teach both of you to be far more patient, compromising and compassionate than you've been in the past. If this friend means something to you, you can probably work things out, but it will take effort as will as humility and self-control.