Is a dnp/arnp qualified to be a counselor as good as a psychiatrist?

It depends: Many nurse pracitioners are drawn to the field of psych nurse practiitioner to be able to do counseling but not all of them. It depends on the state requirements for their training and their personal background. Ask the np directly and some other counselors in the community.

No, not generally: Some nurses have backgrounds in psychiatric nursing, and then become nurse practitioners. Some have also taken more psychotherapy training beyond their nursing degree. As my colleague suggests, you can ask them directly about this. But please remember that psychiatrists have full medical and psychiatric training -- which includes formal education and supervised experience in psychotherapy.