Chaplains have shown better than psychologists.
They’re both good, but chaplains have a very different type of duty compared to police psychologists.
“Police psychologists conduct pre-employment screenings for police personnel, fitness for duty evaluations for police officers, and how to work in crisis situations like hostage negotiation teams/hostage barricade team.
“The police psychologist teaches police officers crime (criminal psychology) prevention techniques, provides clinical counseling to police officers and their families. Police psychologists help police officers deal with trauma and stress through clinical counseling. Counseling programs include resilience, life skills building and peer counseling.”
Importantly, police psychologists frequently need to testify in court, which can often present a problem for chaplains. Psychologists can present clinical evidence.
Now this being said, police chaplains are also very helpful in ways complementary to police psychologists. For example, they are superb for bereavement counseling, any religious “interface” within the department or the community (which can happen a lot), they can conduct marriages and funerals, as well as marriage counseling. They are also very in touch with department morale, acting outside of the chain of command to troubleshoot problems and perform an ombudsman role.