Goku believed Vegeta, but spared Frieza anyway. Because Frieza put up a good fight or was pathetically groveling.

It's mostly the former. One of goku's only character traits is that he wants to fight strong people. It literally doesn't matter how evil they are or what they do while he isn't looking. As long as they can potentially come back and give him a good fight later, he'll do everything he can to avoid killing them. Which doesn't even make sense considering in this universe literally no one ever truly dies. Even dead people can keep training and come back later to give him another fight. But that's his logic. Weaker than me? You can't do anything terrible to me and my friends anyway so why kill? Stronger than me? That's fun, so why kill?

If, like Vegeta, they eventually become domesticated and stop doing evil shit, all the better. But if not, oh well.

It's also contradictory to some extent, too. When Cell kills him, he decides to stay dead so that people will stop coming to earth looking to fight him and endangering his friends. And then he only comes back because he realizes that doesn't actually keep earth safe. But then we get to Super and he's just threatening every living thing in several universes with complete annihilation in order to have a better fight.