In my state, the purchaser is responsible for the "supplemental tax," where the property tax assessment is "trued up" on the purchase price. The escrower only pays the regular, secured property taxes out of escrow.

Occasionally buyers here are surprised by this. I had to pay 6 months of stepped up tax basis on my own after buying, but I knew it was coming and had budgeted it. Then you know how much your property tax will go up every year, thank you Prop 13. . .

It depends on how well you track your finances, your level of discipline (will you in fact budget 1/12 of your property tax every year? Will you budget extra in case your insurance goes up?

I just stopped my escrow account because I can handle it, and I like being responsible for paying taxes when I want to and not worrying that a third party is going to mess them up. But I've done this all before.