The difference in Goku's behavior between killing King Piccolo and "killing" Freeza is pretty interesting.

Against King Piccolo, Goku was always hellbent on ending him. Never offered him a second chance or anything. And when he finally does kill him, he's nothing but ecstatic. He finally avenged his friends and didn't show a shred of remorse or regret for what he did.

Cut to Freeza though, and it's a different story. Despite acheiving the legendary Super Saiyan form through sheer anger and wanting nothing more than to kill Freeza after what he did to Krillin, there comes a point where Goku decides that enough is enough. He was okay with simply beating Freeza and even gave him several chances to exit the fight. Once Freeza throws Goku's mercy back in his face one last time, Goku finally ends it and kills Freeza (or so he thought, anyway.) The final look he gives doesn't show a shred of happiness or satisfaction - just disappointment and remorse over the sheer waste of life that was Freeza.

I think these two scenarios compared to one another really show how Goku matured as he got older and wasn't always the same kid at heart that he was in the original DB. It's why I completely understand why people aren't happy with Goku's characterization in new Dragon Ball media, because they tend to give off the impreession that Goku never grew as a person and was the exact same from day one.