Neither. Or both, perhaps.
I've moved around quite a bit... and come from both a medical background and family... so I shop.
The doctors I go with (GPs and specialists) I TALK with. We can discuss various forms of treatments, differentials, supplementary treatments (counseling, nutrition, etc... they'll send out to a specialist, but then work as a team with the specialist), probability, pathology... whatever.
So once I've selected my physician, I never go behind their backs, as it were. We discuss things right there in office, and if I come across something later on, I ring them up and discuss various alternatives over the phone -or if needed, come back in.
Once I've found that one great practitioner, I'm pretty much set. Because especially in medicine, birds of a feather really do flock together. Once I've found an intelligent, communicative, great doctor... they're friends with the other great doctors in the area in various specialities.
The ONLY specialty that I don't do this with is surgeons. Brilliant surgeons are often terrible people, or at least terrible WITH people. I don't care about who a surgeon is as a person, by and large. I care with their skill with a knife.
ROFL... Oh, my, goodnes though... I forget what being with a mediocre doctor is like. Every once in awhile I'll need to take an 'on call' whomever. Oy. After months of hospitalization with my son (and a crash course in pulmonology, Children's Hosp docs REALLY work with and educate parents to be part of the treatment team... I would get called in to look at new chest films and discuss various antibiotics, just like every. other. parent. with a long-term kiddo... in on every treatment, trained to do treatments at home -respiratory therapy, PICC Lines, vitals, etc.) we had an outpatient appointment with someone who not only didn't get my son's diagnosis correct... they went on (in very slow words) to tell me that asthma (which my son doesn't have) makes it difficult. for. him. to. breathe.
Blink. Blink.
I'd asked a simple question, that was completely ignored, and was then treated like I was 4 years old. Never went back to HIM again!!! (and scheduled a repeat of the "same" appointment with someone else). Sure enough, not only had the doctor treated me like an idiot, but had been an idiot himself... missing some really key things that had come up and needed to be immediately addressed.
So... for me... it's the working relationship that is the most key. If I don't have that, I don't stay with that doctor.
But, yes, I also do my own research. Asthma, for example, has over 80 differentials. Doing a crash course in the possibilities we were facing and looking at made it possible for me to have an intelligent conversation. But once I'm able to understand what's up, then we work together.