Both hospitals have poor reputations. I am fortunate enough to have never had to go to either but I think BRMC would probably be slightly better. I have had occassion to visit people and am appalled by some of the things I have seen. One woman I went to see at PCH had bloody bangages that had been removed and just thrown on the floor around her bed.
I had another friend who ended up after two weeks in PCH at Cleveland Clinic having open heart surgery to remove valves damaged by an infection in his leg which had spread. They had diagnosed it and were treating it as blood clot until he spiked a fever. They sent him by ambulance at that point to CAMC. He is also going to lose his leg now.
I think they usually are aware of their limitations though and have medivac capabilities.
You can check them out Health Grades. They have pretty low ratings in almost every area.
HealthGrades - Research Hospitals, Doctors and Nursing Homes
Having said all that, there are some excellent doctors who practice at both hospitals. I think for routine health issues which most people encounter, they are just fine. Personally, if I had some serious uncommon disease, I'd go to Bowman Gray or Duke or somewhere like that.
And I also think that you can pick any hospital in the country and find incidents of misdiagnoses, etc. So it wouldn't be a deal breaker for me if I were moving here.