I was wondering if anyone here was aware of any studies that compared the efficacy of shaman medicine such as ayawaska with current treatments for psychiatric disorders such as anxiety disorders. I have read numerous anecdotal reports on its use but was wondering if there were any studies comparing such treatments.

As far as I know, some of the psilocybin studies used participants that were labled as incurable by conventional psychotherapie and medication. Maybe you can go through the MAPS archieves and look what study design and participants they used.
I certainly remember reading in "Realms Of The Human Unconscious" that many of Stanislav Grofs patients went through all possible therapeutical procedures at that time without much benefit, and made astounding progress in very few sessions with LSD.

So this is definitly evidence, that these compounds can help in cases, where conventional medicine has given up.
I don't remember any study that uses a psychedelic therapy / psychotherapy / control group approach or something similar. But since this is an obvious thing to do, there could be a study that already did it