Biggest trouble I've had with the VA was getting an initial appointment with a primary care doctor, and then again the next two times I moved and had to repeat the process at a new hospital. Once I had a primary care doc though it was always quick and easy to get seen by specialists or to get follow up appointments with that doc.
As far as benefits go, it can be a lengthy process, but they back pay to your application date or your separation date, so in the end it's relatively neutral.
But for care you can always walk into the clinic and be seen immediately.
The VA gets a lot of ****, rightfully so usually, but I and most vets I know have also had positive experiences.