At the top end, this will be true. Surely, a well-trained surgeon is a well-trained surgeon and mechanically they should all have roughly equivalent skills. The difference lies in experiential knowledge: knowing what to do whilst in a surgery, based on practical experience and seeing similar patients. We've interviewed four of the top pediatric cardiology centers in the past two months, searching for the best treatment option for our daughter, and only 1 of them has a research focus in the needed area, accompanied by a specific treatment protocol and specifically trained staff. That's not because the other hospitals are "worse". It's a result of our daughter's need being extremely rare, with very low demand. Even the above-mentioned hospital only sees ~1 patient per month (compared to maybe 1 per year or fewer at the other hospitals).

I 100% agree: experience is key ... but so is a clinic's/hospital's internal investment in any given speciality. And if it's a teaching/research hospital, so then is publishing by its clinical experts.