I'm definitely less familiar with the Amish, so I did some looking beforehand. What I was finding that their willingness to use modern medicine, or to use it preferentially, is said to vary a lot from community to community.
As well, I found they self-fund access to healthcare, and I have no idea what the dynamics would be like with that--would you decide not to see a doctor so you're not placing a burden on your neighbours?
Neither's a factor with Hutterites in Canada. They're very willing to use and rely on modern technology (they probably have some of the most technologically advanced farming setups you've seen, have cell phones, etc) and there's no cost barrier to accessing healthcare.
I was curious, shared what I found. Take from it what you'd like!
Except the Amish have access to modern medicine and there are modern studies investigating their population level disease rates.