I'm at a site w/o residents. It is honestly demoralizing the level of apathy I see and deal with on most of my rotations. Some docs are well-intentioned, but others do not care. And I don't blame them most of the time. I chose to pick a site that was in my hometown so that I could live at home and decrease costs especially since my parents are going through some financial hardships. In hindsight, it was a mistake I think. A few of my friends at other sites, especially those w/ residents, seem to enjoy not only stronger clerkships, but better teaching. None of my NBME shelf scores have been above average and that is likely related to my sh**ty rotations.
Now, I have worked it out to my own personal benefit in that I am interested in EM, and, for instance, during my psychiatry rotation we were assigned to the facility and were expected to float between different docs. I rotated w/ a doc who I knew personally who he gave me autonomy (did my own H&Ps, etc.) for three days only. He did my evaluation. The rest of the rotation I either took off or went in to a local ED w/ an adjunct faculty attending and did like 9 shifts or so. During my Surgery rotation, I split a 4 week with an anesthesiologist I was also friendly w/. Unsurprisingly, those encounters have been my favorites. The rest of my M3 so far has been average to below average to terrible. I did my pediatrics rotation in an outpatient setting and the doc would only let me do a PE on the patient, never let me do my own H&P. Nice guy, but pretty average rotation.
Don't fall into the same trap that I convinced myself. Go to a site w/ residents. I had told myself the same, but at the last minute, decided to come home for better weather, comfort, and familiarity. I would say it has largely been a misfire, but I try to remain optimistic in that I have more free time for wellness and that most of M3 for most people in the DO world is not great relative to MDs and even for MDs, it's not all sunshine and roses (especially for Carib folks). Glorified shadowing is part of the game, just much more prevalent for DOs (not only in my experience, but based off SDN, reddit, and speaking w/ classmates). I should have gone w/ my gut because I had a decent shot at ranking and matching at a program w/ a few residencies, but also a well-established system that had been taking students. I'm grateful, though, I have a good Step 1 score (243), that will hopefully negate the bumps I expect to endure during M4 auditions if I choose to do something outside of EM or anesthesiology. But, in short, I think this will hurt me.
/rant
edit: But to again reiterate and help answer your question: go to a place w/ residents. I would rather not do much during third year, but learn, than do scut work and not learn. I felt I did a lot of scut work on my Surg rotation, didn't really learn about processes or pathology. That's my 2 cents. Ideally, you go somewhere where you do stuff and also learn, but -- and I say this only based off my friend who attends a respectable MD school w/ a great hospital w/ a ton of residents -- that even MD students do their fair share of shadowing, but they have better didactics (eg. weekly conference etc.).