Depends what experience YOU want. Ultimately, try both.
One shouldn't be easier or harder to acquire as compared to the other.
If you want to be in a Docs private office in handsome medical building, from 9-6, seeing patients all day, as he/she is, then go for private practice. (I over generalize here).
If you want to be in the academic teaching setting of a university hospital (I over generalize here too) then call the Univ. You'll see more Med Students, Residents, Fellows wandering the halls, and see what the teaching side of medicine is about while you see patients and you might even get pimped as you stand next to residents. Watching your future in your eyes. This is what academic docs love: teaching. Which is what I love about it. You'll also may access to ORs you won't have in PP. (generalization again.)
I prefer the latter scenario for personal reasons. Having made the ask, I start in a Private/Teaching VERY prestigious and well known hospital both in US and Intlly on Monday. Anesthesia. I'm in the door through their observership program that is really limited to Med Students/Residents. I just asked to shadow, so I'm happy with however I gained access. In April, I will be at the local Univ Hospital/Med School taking a 2 week rotation in an Anesthesia subspecialty that is also normally limited to visiting medical students. But having sent a COLD email to the Dept Chair to shadow, he said he'd arrange it, and this is how it's going down. Both of these spots are really reserved for Med Students doing away and elective rotations, the "try out" rotations you take to get in with a residency spot. It was hard explaining myself to those that the Chair CC

, but it happened. So, instead of making friends during med school to help with residency, maybe I'll make friends during pre-med to help with med school.
😀
It's all about timing, how you ask, a little background, etc etc.
Have a great turkey day everyone! Hope this helps this thread.
D712