Sasuke VS Naruto battle...people got that confused..alot saying chidori peirced through Rasengan......its not that.....im pretty sure chidori didn't litterally win...It was Sasuke that dodged Rasengan with Sharigan. Sasuke could c Naruto movements...He dodged it...He tricked naruto when he said, "Lets make this on our final attack," knowing that his Sharigan can dodge Naruto. It was a not so smart thinking in naruto's side...but Rasengan is much more stronger... than Chidori...Rasengan has more powerful because Rasengan can increase in power,velocity...u could always mold more chakara into Rasengan....You dont need speed to complete it. Chidori it like a powerful Edge...and Rasengan is like a Bomb...

and compare this....Chidori is like jounin lv jutsu while Rasengan is a Kage Lv jutsu...
Tsunade, Orochimaru, Ero Sannin acknowledge Rasengan more than Chidori. They know its a really powerful jutsu..because it was the 4th Hokage's jutsu

and u saw the comparision of dmg made in the first fight of Naruto VS Sasuke when Kakashi stoped them both from coliding and they both hit the water tank...Rasengan is more destructive...