I saw that Naruto got very angry and unconscious when Hinata was hit by Pain. This made him lose control and Nine Tails took over. Still Pain looked happy as if he wanted that to happen. Naruto on the other hand has to get back control in order to defeat Pain.
Well, it all depends on who is in control and what their objective was.
When Hinata was stabbed in front of Naruto, he became angry and due to his anger, he went out of control. He was in need of power to save Hinata and would have done anything to get it. Which is the very reason why he gave up the control of his body to Kurama.
When Kurama took control of Naruto's body, Kurama was not trying to defeat pain. Rather he was trying to break out of Naruto's body. Which is generally the trend to any tailed beast and Pain knew that. Since the beast will be busy breaking out, capturing the beast would be much easier. Which is why he pushed Naruto to go berserk.
That is why Minato stopping Kurama's seal to be broken at the end and giving him the control of the body back to Naruto was that important. Because by that time Pain had exhausted a large amount of Chakra doing his planetary devastation attack. So it was the ideal time for Naruto to take the counterattack before Pain could regain his complete power.