Is there a way to compare treatments for medical vs psychological issues?
I would say no because we aren't looking to compare medical treatments to psychological treatments. It isn't possible to do so and there isn't any real world application for such a process, i.e., it doesn't tell us anything useful.
The question I think you're getting at is:
Can we show that a treatment for a psychological disorder is effective at treating the psychological disorder, in the same way that we can see that a medication is effective in treating a physical disease/disorder?
The answer to that question is absolutely!
When we implement a treatment for a psychological disorder we are often hoping to reduce the symptoms of that disorder, rather than finding a cure. When we are looking at the effectiveness of psychological treatments we are looking for a statistically significant difference in measured behaviours from before treatment to after treatment. Researchers in the paper linked below used 4 treatment conditions to (1) determine if treatments for depression were effective and (2) to compare the effectiveness of the treatments against each other (Elkin et al., 1989).
The statistics can get very complicated when it comes to showing effectiveness of treatments.
I believe that it is extremely important to note that many psychological disorders are life long and many people can experience a wide range of symptoms that vary in intensity for their entire lives. So, to bring it back to your original question, psychological disorders don't have an easy 'cure' the way that some physical diseases/disorders do. Seeing a counsellor/therapist/psychologist for CBT Treatment does not have to mean having a life long relationship with a counsellor/therapist/psychologist. The treatment includes learning skills/tools to cope with your situation and if CBT is successful the person can end therapy whenever they have learned enough skills/tools to live a full and healthy life.
Elkin, I., Shea, M. T., Watkins, J. T., Imber, S. D., Sotsky, S. M., Collins, J. F., ... & Fiester, S. J. (1989). National Institute of Mental Health treatment of depression collaborative research program: General effectiveness of treatments. Archives of general psychiatry, 46(11), 971-982.