Psychologist here who was part of the admissions team at one of the top medical schools for several years and has done a fair bit of med student/resident education.
Raw acceptance rates certainly favor psychology being more competitive but I agree there are multiple factors at play here. Med school admissions are a lot more formulaic - you won't necessarily get into top programs, but if you tick the boxes I think odds are very, very good that you can get in somewhere while that is not necessarily true in psychology just because of how the admissions process works. That said, most of the "virtually a requirement" boxes are harder to tick for medical school than psychology. Medicine has done a better job protecting the educational system - the bottom rung prof schools lower the bar significantly in psychology - its an issue in medicine too, but not as widespread. Admissions decisions are based on completely different things though. When doing med school admissions I was encouraged to weight GPA much more heavily than I would have in a psychology program...a 3.9 GPA applicant was heavily favored over a 3.6 applicant. That difference is not completely insignificant in psychology admissions, but much less important given other factors take precedence. At the same time, what was considered "good" research experience for medical school (ignoring MD/PhD candidates) would fall somewhere between mediocre and utterly pathetic for psychology programs. In line with my earlier comment about "ticking boxes", medical school places more emphasis on markers over actual experience. Ironically "pubs" actually mattered more for medicine for this reason because no one looks that carefully at how deep the experience was. Those of us who have worked with pre-meds certainly see this - people crawling all over each other fighting to get their name on something by doing obscene amounts of scut to get "hours" without wanting to put in the effort to actually learn how to do anything. There is more emphasis on hours of doing things than what is actually done in those hours. Don't get me wrong - it does matter to some degree, just less than it should. All that said, I do think it makes top-top MD candidates overall stronger than the top-top PhD candidates I have seen just because they were more well-rounded. That said, we're talking about probably the top 5% of people who were admitted to a top program. Beyond that, it largely seems a wash. This continues in education. I've taken special courses in how to teach med students and the core take-home is "Don't make them think, they don't want to and aren't good at it - just give them stuff to brute-force memorize". Psychology education is often too far in the other direction (in my view) where things get discussed ad nauseam but no conclusion is made. It continues in the professional world where MDs make fun of psychologists for being wishy-washy and not being able to give clear off-the-cuff answers to even simple questions and psychologists make fun of MDs for being unthinking automatons who can't do anything unless someone else hands them an algorithm explaining how.
TLDR - Programs focus on different things. I don't think getting into either type of program is a major accomplishment in and of itself. Anyone of modest intelligence who really wants it and is willing to do the work should be able to succeed eventually. It may take strategizing and those strategies will be different.
