Urk. Seymour is a pain in the butt. For one thing, he has a creepy face and sounds like Winnie the Pooh on crack. For another thing, he was cruel and evil to his mom, who only wanted the best for him. For yet another thing, he acts all nice and polite so people don't get that he's evil until the very last minute. Oh, and did I mention that he WON'T DIE? You have to fight him five gazillion times, and he keeps coming back with his stupid machinery to challenge your party again and again. And whenever he kills you he makes a big speech before hand, so when you die, you have to listen to his stupid speech ALL OVER AGAIN. He annoys me greatly.
"Ah, Sir Auron. It is an honor. I would be most interested in hearing what you've been doing these past ten years."
Seymour is a maester, which means he has super exceptional power over the people. He also happens to be insanely corrupt and evil. Luckily you get to kick his ass. Unfortunately you have to do so many more times than allows for one to maintain one's sanity.
Seymour drops the first hints that Auron isn't all he seems. In between trying to marry Yuna, he tells the cast he can sense the Farplane from Auron. Auron's repsonse is a loud "hn" and a refusal to comment any further. Translation: he knows Seymour isn't all he seems, either.
Other than that, there isn't too much interaction between the two directly, although Auron seems very concerned about how Yuna intends to deal with the situation with Seymour. When she tells him she intends to marry Seymour to make Spira happy, Auron darkly comments, "That's not good enough." Nevertheless, he lets Yuna take care of it, though he tells Tidus in no uncertain terms to keep an eye on her.
In a lot of ways, I think Seymour represents the corruption of the Yevon-inspired system Auron has decided to turn his back on. It's not just that Auron seems to dislike Seymour as a person; he also sees Seymour as an example of the worst of what Yevon can do.