Well I can't comment on Dr. Klimas, but I have seen Dr. Peterson for a few years. Here's some things to consider:
His office is located in Incline Village, NV which can be easy or hard to get to depending on where you live.
Dr. Peterson + staff have tons of experience with ME/CFS and is a very caring doctor. His initial workup is very thorough and includes infectious disease, immune markers, lumbar puncture, MRI, cardiac, and treadmill tests to "quantify" your fatigue. I doubt I would have been able to get another doctor to do this kind of workup on me, or if I did I'm not sure they'd know what to do with it. Dr. P's experience is huge here and its a big value to seeing him.
My insurance paid for most of the workup. I would think it would be expensive if you didn't have insurance. Some of the immune markers he tracks are still considered "experimental", so insurance coverage would be hit or miss on those. He also takes medicare.
With my case, he found several abnormalities but no "smoking gun". He has tried me on several empirical therapies which have not been successful for me. He appears very familiar with various anti-virals, but since I never have any quantifiable viral activity I haven't been put on them. I have not tried Ampligen, but I'd imagine his patients have a good shot to qualify for the open label trial as his office is a site.
He's pretty risk averse when it comes to treatments so that's good for safety's sake. I'd say he has a healthy skepticism of the "drug/bug of the month" crowd. If you want to jump on the latest thing before there is much in the way of evidence, it might be a frustrating experience. He has been around a while and knows the ins and out of dealing with disability companies with respect to ME/CFS. His patients are well characterized and he is connected with ME/CFS research community (what exists of it) so his group is given the opportunity to participate in research projects going on in the CFS field. (ie his patients in the XMRV studies, etc..)
The only frustrating aspect of my experience with him is that sometimes communication and follow up is harder than it should be. He is essentially a small town/one doctor operation. He travels a lot to meetings. I'd imagine if you are a local CFS patient, it would be pretty smooth as you could just have regular appointments with him and follow up that way. But at a distance, communication can be inconsistent and getting your lab results can involve delay. It often takes multiple contact attempts to get a response. This has gotten better lately as they have hired a research assistant who is very organized. To be honest, he and his staff have always come through for me when I have needed them so I can't complain much, but in this area his office could use some improvement.
The thing to understand is that even though hes probably one of the best in the field of ME/CFS and hes a very caring doctor, nobody knows the cause of ME/CFS. Even with all of the testing he does, he doesn't always know what it means (for example, I have cytokines in a certain pattern and all he can tell me is that a subset of his patients also have this, but he doesn't know why). Its still pretty trial and error to see if you will respond to any treatment he has.
I'd suggest that if you go to see him you should submit to his whole workup. He may find some treatable illness and you may get better. If he diagnoses you with ME/CFS, then I think its worth leveraging his experience trying some of the more empirical treatments he has.