Although Lucifer resents his label as the King of Hell -- to the extent that he abdicated his throne to play Detective in L.A. -- he's only grown more capable as a leader after spending time around humans, better understanding mercy, forgiveness and accountability. Sabrina, on the other hand -- a teenage witch who grew up around Greendale mortals -- consistently shows that her righteousness and desires are more important than humanity, going as far as to create a time paradox so she can enjoy her teenage Earth years. If the Iron Gates must stand, Lucifer should stand behind them, not Sabrina, who still has a lot of growing up to do.
In Season 1, Episode 1, of Lucifer, Lucifer Morningstar is a hedonist, intent only on finding pleasure as he operates his nightclub, Lux. However, after he witnesses the murder of Delilah -- a pop-star his devil's bargain made famous -- he feels burdened to find her killer. Although he left his role in Hell five years ago, we see a glimpse of Lucifer's penchant for punishment as he gleefully tackles the gunman who shot her. However, the gunman says, "I just pulled the trigger," suggesting that someone else is the true culprit.
This moment leads Lucifer to interrogate Detective Chloe Decker at the scene of Delilah's murder. When she erroneously equates Delilah's death as a drug-dealing mishap, Lucifer becomes determined to find the real culprit. He abandons his full-time reign of Lux to become a part-time consultant to the L.A.P.D. to avenge Delilah's death. However, one case quickly becomes many more as Lucifer gains a sense of purpose he never had in Hell nor on Earth.
In Lucifer's Hell, humans exist in a prison of their own making, a loop of guilt-fueled fever-dreams that he has to watch for all eternity. He watches them make the same mistakes again and again, never choosing a different path because they don't think they deserve it. Also, he has no power to stop them from entering Hell. However, in the interrogation room, Lucifer can make a difference, using his Demon/Angel skill to articulate others' desires to help the L.A.P.D. understand why crimes are being committed and stop future ones from occurring. The L.A.P.D. teaches Lucifer to have an active role in human affairs.
In Season 1 of Chilling Adventures of Sabrina, Sabrina is wholly concerned with her upcoming Dark Baptism that asks her to sign her soul away to the Dark Lord. Having grown up, for the most part, as a mortal, she's not ready to sign anything that could jeopardize her mortal life -- her boyfriend Harvey, her friends Roz and Theo. Even though this choice pains her aunts -- who in the interim lose their powers. Ultimately, she does sign her name to the Book of the Beast as a way to defeat the Greendale Thirteen -- angered witches who were sacrificed by mortals centuries earlier -- giving her the power to summon Hellfire.
By signing the Book of the Beast, she saves Greendale, but it only shows how flimsy Sabrina's reasoning was to not sign the Devil's book. At the first sign of a true threat, Sabrina reneges on her value to gain power. There could have been a Sabrina who instead of banishing the Greendale Thirteen perhaps reasons with their tortured spirits -- since she knows how difficult it is to be sacrificed for someone else's plan -- and together defeat the Red Angel of Death.
Unlike Sabrina, Lucifer is cautious with his power around mortals. He reserves punishment -- like showing his Demon face -- only to those that are wholly unrepentant. However, when mortals are in danger, he will use his powers -- such as what happened to Delilah's killer, who tried to kill Chloe and is driven insane by a glimpse of Lucifer's true self.
Sabrina, however, sees magic as a way to fix the past. When her then-boyfriend, Harvey, loses his brother in a mining accident, Sabrina resurrects him. Inevitably, he becomes a violent zombie that Harvey is then forced to kill. Sabrina doesn't think about the consequences of her actions and inadvertently causes her boyfriend to lose his brother twice.
The ultimate difference between the two is how love changes them. In Season 4, Episode 10, once Lucifer fully accepts that he loves Chloe, and she knows who he really is, he is also forced to choose between being with her or returning to Hell to ensure demons don't keep on escaping to Earth. He chooses Hell. Due to loving Chloe, he's gathered affection for the rest of humanity and wants to ensure that Chloe and people like her will be safe.
After Sabrina's boyfriend Nick sacrifices himself to the Devil to save the world, Sabrina brings him back to Earth. Throughout Season 3, Nick turns to vices to cope with being possessed by the Devil. Although Sabrina believes she saved Nick, she really just retrieved who she wanted, no matter the pain it caused him.
Despite having no knowledge of Hell politics, Sabrina allows her past self to rule it. This decision was made only so she could reside on Earth without the responsibility technically of overseeing Hell. Despite all of her Season 3's ambition/drive to defeat Caliban, she gives up actually ruling Hell once she "wins."
Similar to Sabrina, Lucifer leaves Hell to return to Earth for love. However, Season 5 shows how he could incorporate his mortal and celestial life to better humanity and Hell. In Season 5, Episode 1, Lucifer visits Lee Garner's hell-loop and becomes inspired to solve his murder. Lucifer could effectively spend eternity like this -- finding justice on Earth for those wronged in Hell and then inspiring those imprisoned below to forgive themselves and leave. Lucifer could embrace the Angel and Demon inside him by living for redemption, showing he'd be a better choice to lead Hell than Sabrina.