When Walt killed Emilio in episode one it was an act of self-defence that happened within the moment, indeed Walt didnt even see Emilio dying. His murder of Crazy 8 was far more intense; it was a gruesome strangling of someone he had gotten to know in the moments prior to the act. You can tell in the aftermath of this episode that this act had a severe impact on Walts soul, after this point you can see that there is no turning back for Walt. He was totally changed by this death and you can tell it haunts him deeply.