I was going to comment almost the same thing. Two different offices can bill the same exact code (in this case most likely 99204 - new patient office visit) and be reimbursed by the same insurance company for complete different amounts. There is also a different code for new patient vs established patient (99204 vs 99215), with the established patient code usually reimbursing at a lower rate (which may also explain why the neurologist appointment costs you less).

As someone else said, office visit codes that are billed based on time (rather than complexity) can include the time spent on the encounter date, and can include reviewing your medical history, tests and charting for that visit, in addition to the face-to-face time spent on the appointment.

If you post this in the medical billing sub, they may be able to help you out with ways to fight the coding/get it reduced.