Short answer: not proven. A recent comparison by researchers reported no greater effectiveness for psychedelic therapy than open-label antidepressants, but it relies on indirect comparisons across separate studies and is not a head-to-head trial: see the summary here. I cannot independently verify the conclusions beyond what the authors present.
Psychedelic therapy is a package of drug, setting, and guidance, which is hard to match fairly with daily medication. Differences in study designs, expectations, and support make simple “which is better” claims unreliable.
At best, current indirect evidence suggests no clear average advantage, but that does not mean the approaches work the same or have the same long-term impact. More direct, well-controlled trials are needed before drawing firm conclusions.
So for now, we cannot say it is better or worse with confidence.