Walt's progression of killing was very different from Jesse's.
Walt managed to kill Emilio with phosphine gas, then strangled Crazy 8 with a bike lock. He tried to poison Tuco but failed, and he then caused Jane to die and watched it happen. Many others died that he was indirectly responsible for, and his brother-in-law Hank was almost killed because of his actions.
All of these deaths can kind of be justified. The first 2 killings were in self defense, as he would have been killed had he not killed them first. He tried to poison Tuco for the same reason, and it could be argued that Jane killed herself, even though it was Walt who put her in that position.
He also maintains distance from all of their deaths. Emilio is on the other side of the RV door to Walt when he dies, Walt is stood behind Crazy 8 as he strangles him, poisoning is a more indirect method of killing (though he never succeeded anyway), and he simply failed to prevent Jane's death. Even though plenty of other people died through his actions, he was never directly involved.
By the time he runs over the 2 gang members and shoots them, he's already made leaps to justify what he has done multiple times, so to go from that point to running over and shooting people at point blank range is less of a drastic move.
Jesse experiences things completely differently.
He is never directly connected to any of the deaths. He simply witnesses the aftermath of them all. He isn't anywhere near when Emilio or Crazy 8 are killed, and he simply thinks Jane killed herself. He needed to get high to even confront the 2 gang members, and then is still saved from doing anything by Walt.
He then goes to Gale's house, looks him in the eye, and shoots a completely defenseless man (who is pleading for his life) right in the face.
Jesse is the only one who is directly responsible for the death, has none of the distance that Walt ever had when he did it, and has barely any justification. It wasn't Gale's fault that he died, it was simply a way to make sure Gustav had no other options.
This is a much more severe progression, so it affects him much more because he has never done anything even close to this. It is a sober, calculated assassination of someone who is completely innocent. This is why it has so much more of an effect on him.