Victator Supreme wrote:The difference being Goku did not really defeat Vegeta. It took four of them and a bunch of luck to survive the battle. Goku had proven himself to be vastly stronger than Freeza. Add in that all of the other fighters were ressurected. Freeza was never going to be a threat to Earth. Also it would of weakened Freeza's holdon his own empire. After hearing of what happened on Namek. It is easy to assume there would be uprisings.
Actually, if mecha-frieza really wanted to, instead of landing on Earth he could just shoot a hundred or more of energy balls from his ship, each one capable of destroying the Earth, to different points in the planet at the same time.
It would be impossible to stop them all, even with Goku`s teleportation.
So Frieza was still a huge threat to Earth.
Even if Frieza didnt become mecha-frieza and was still missing his legs and arm, he would still be a huge threat. As long as he could recover to his previous or approximate strength he would not need his legs or more than an arm to shoot those hundred or more energy balls.
Goku doesn`t like to take lives when he doesn`t have to (what he considers have to is "if I dont kill him right now he will kill me right now"). Besides that, he knew that it would be very humiliating for Frieza to be defeated and be spared by the Super Sayan. And he had a very selfish reason to let him live... He liked having an opponent of his caliber around.
Those were the reasons why Goku acted the way he did. The smart thing would be to kill him. But Goku thinks everything but smart.
Regarding Vegeta it was exactly the same reasons, except maybe humiliating him, since Goku and his friends didn`t win because they were stronger than him.