I find that INTPs of my approximate level of intelligence tend to form a symbiotic kind of mutual understanding with me.
They see me as a little stubborn and not quite as objective or logically discerning as they are (though still moreso than the average person, which they seem to like), but they tend to admire my social abilities for their strategic value and appreciate my out of the box thinking. They know I'm great for brainstorming and I know they're great for checking logical and theoretical consistency from a broad overview kind of perspective. (They'll also discuss the implications endlessly for no real reason, which I love to do, and which NTJs don't seem too interested in.)
So, I don't feel any particular kind of rivalry with INTPs. There's a little *friendly* rivalry with certain ENFPs, but really we love each other (even if other ENTPs won't admit it.)
You should pit some seriously different types against each other--how about some complete opposites?
I vote INFJ vs. ESTP. That'd be a riot.