There never was much they could have been rivals over, was there? X killed Sigma first, so the only thing left is to see who can kill him deader, or who kills him last and makes him stay dead. Since X was content to stay a B-class for so long, he can't even be interested in competing with Zero for Employee of the Month.
I'm surprised at how much credit it gives Zero for helping to make X what he is today. Light built X with great potential, but nothing guarantees X would ever achieve it, and here it says it's thanks to Zero that he did. They don't use the word senpai, but to me it seems to fit.
And, skipping ahead again, there's an interesting parallel: Zero is trying to make X into the Hunter who will surpass him, and Sigma is trying to make Zero into the Irregular who will surpass him.
The whole of X's profile shows only 2 scenes of him with Axl, and he's so grumpy in both of them! I don't have X7 and I've never played it, but it looks like it would get annoying very quickly. And I'm a bit disappointed in X, for all his talk of pacifism he can't even get along with one other individual. (Reminds me of the line from Peanuts, "I love mankind! It's people I can't stand!" ^_^) He's leaving it to Zero to play mentor/senpai again.