Most people don't know but you can get the best of both. You can push for what called "community care" through the VA. If the VA admits there isnt a VA doctor close enough to you, they will send you to a private doctor of your choosing and pay for the whole thing.

I was able to get back surgery by the best doctor in the region this way. I refused to work with the VA doctor due to a bad appointment. I waited weeks to see this doctor and he spent 5 minutes looking at my chart to say I was too young to be helped. Could've just told me over the phone. Went back to my primary and complained and they signed me up for community care since they were the only other in the area.