I never understood why the murder of a police officer was viewed by some as significantly worse than other murders. In my mind, both are equally horrible.

@barking, your comment made something click. For police, the protection of police officers is by far their highest duty, and then much lower is the protection of the public. From this first principle, I can now see why it follows that the murder of a police officer is viewed as much more important, and why so many more police resources are used to solve that crime.