Yeah wow you're seeing some differences! Welcome to New York!
I work in NYC but I own properties upstate near you. When I buy I don't care what the assessed value is (well, that's a bit of hyperbole, but not much). I study the market and cash flows (since these are investment props).
If you're trying to figure out a sales price to suggest to a client, which seems to be your situation, then you need to do a comparative market analysis that includes a thorough study of recent sales, list prices and prices of homes in contract. I'm afraid there aren't many shortcuts or formulas that you can rely upon.
And that's in a normal market. This in my opinion is not a normal market. You've just got to have your ear to the ground as much as you can.