I tried a functional doc and didn't get anything of value. On the other hand, I've had a hard time getting anything of value from a non-functional doc.
I think about the difference like this:
1) Regular docs ae hampered in treating us by an unpleasant mixture of prejudice and ignorance about our disease. For them, our disease is "all in our heads", caused by fear of exercise and deconditioning, or is really anxiety/depression that we can't admit having so we claim it's ME/CFS instead. But, if they would let go these biases, they could bring the full weight of science and modern medicine to bear on our illness. That's no small thing- look at everything that's been done with HIV once AIDS patients made the world get over its prejudice against them.
2) Functional docs are hampered by their perspective on medicine and illness. I strongly suspect some of their fundamental beliefs about how illness works are wrong; e.g. complex diseases don't have simple root causes, precision medicine isn't yet far enough advanced to personalize treatments in the way they suggest, we don't all need to detox, inflammation and nutrition aren't unitary drivers of illness. They may listen better than regular docs, but they don't have the treatments. With detoxing and reducing inflammation with a particular diet and other functional treatments, you would still die of AIDS if you didn't get the antiretrovirals from the regular doc.
Here's a pretty functional medicine website with the treatment approach outlined:
https://triadhealthcenter.com/chronic-fatigue-syndrome-a-functional-medicine-experts-guide/
You'll notice that the last "treatment" is Gradual physical fitness- sounds like GET to me! Other treatments are generic advice any doc would give- eat well, get enough sleep, destress. And some treatments are just silly and not really how the body works- like changing how your mitochondria function based on how you eat. If you want real info on diet and mitos, see a mito disease website like mitoaction.org. It's really not about eating more grapes and flavanoids as the functional doc says.
Given this, I don't find much to value in functional medicine. Maybe others have had more positive experiences.