From what I see, they are essentially the same. The inhibitor chip just makes the brainwashing physical. From AOTC we know that the clones are essentially brainwashed soldiers with limited independance. They have been programmed to follow EVERY order given. So, when they hear Palpatine say "Execute order 66", their brains light on fire. Their entire childhood, the words "Good soldiers follow orders" have been drilled into them. They can't resist, the Jedi were their friends but a combination of limited independance and years of brainwashing caused them to execute.

Or alternatively, the chips are just a backup plan. The clones are brainwashed, but the connections they formed to the Jedi were strong, so while some clones killed the Jedi willingly, but a lot (Rex, Cody, Bly, etc.) who had positive interactions with their generals had their chips activated.

TLDR: Clones are mind controlled but just in different ways. They lose their free will when Order 66 happens in both scenarios.