Tidus and Auron are different in almost every way. Auron appears tough and strong while Tidus cries. Auron is quiet and reserved while Tidus is very talkative. Auron is content to travel alone, while Tidus needs to be around people. The two have one important thing bringing them together: Jecht. Auron is in Tidus' life because of Jecht, and he makes Tidus a stronger person for Jecht.
Auron and Jecht were both guardians for Yuna's father, Braska, when he defeated Sin ten years prior to the events of the game. At the end of their pilgrimage, Jecht volunteered to become Braska's final aeon, to rid the world of Sin for ten years, bringing about the Calm. Jecht knew that he wouldn't get back to his Zanarkand or see his family again, so he didn't have a reason to keep living. He still cared about his family, though, so before they defeated Sin, Jecht made Auron promise to find Tidus and watch over him. Although Auron didn't know how he was going to get to Zanarkand to keep his promise, he consented.
All right, I will! I give you my word. I'll take care of your son. I'll guard him with my life.
After Braska's final summoning, Auron was so filled with rage for losing his friends that he went to Yunaleska (the fayth who tranformed Jecht into the final aeon) and attacked her. He was so mad at her for continuing a cycle that he knew was just a waste of life, and he wanted her to pay for his friends' lives. Yunaleska was too strong for Auron to handle alone, though, and she killed him. Rather than go to the Farplane after he died, Auron chose to remain an unsent. In his mind, he couldn't move on because he still had a promise to keep to Jecht.
I guess since Auron was killed once, he couldn't be killed again. That gave him the freedom to approach Sin, his buddy Jecht. Auron figured out that Sin was the link between Spira and Dream Zanarkand, and used Sin to get to Tidus. I think Jecht as Sin even helped Auron get to his son. Auron looked and spoke to Sin at the beginning of the game. This leads me to believe that Auron was somehow able to communicate with Sin, which supports my idea that Jecht as Sin willingly helped Auron get to Tidus. Auron probably used Sin several times to check on Tidus before Tidus was seventeen. Tidus knew Auron from his childhood, so it definitely seems like that is the case. Auron's last visit was different, though.
In his last visit, he came to take Tidus to Spira. Jecht wanted Tidus to defeat him and end his suffering as Sin. He was able to communicate that to Auron somehow, as Auron is the one who eventually tells Tidus what he must do. I think that's what Jecht was telling Auron at the beginning of the game when Auron asked, "Are you sure?" before Tidus ended up in Spira, 1000 years in the future. It's obvious Sin was telling Auron something, and that makes the most sense to me.
Auron took his promise to Jecht very seriously. Not only did he watch over Tidus and help protect him, he tried to make Tidus the best he could be so that Tidus could protect himself, and so that he could eventually defeat Sin. With Jecht gone, Tidus needed a father, and I think Auron definitely filled that position. Like with Jecht, Tidus butted heads with Auron a lot. Tidus also yelled out in frustration at Auron a couple times, and the only other person he yelled at like that was Jecht. The two really cared about each other, though. Tidus looked up to Auron for guidance, and was genuinely happy to see Auron in Zanarkand, and when he met back up with him in Luca. Auron looked at Tidus as his project, and helped shape Tidus into the man he had become by the end of the game.
I must admit I was worried at the beginning, but you've done well.
After defeating Sin, and having finally completed his promise to Jecht, Auron is sent by Yuna. He's happy to be sent, stating that it's been long enough. Tidus shortly follows.