You will want to go with the county assessor's office figure. It doesn't matter if your lender(s) made a mistake(s) on your Form 1098, or not. What truly matters is how much you actually paid in property taxes during the last calendar year. That is the root source of you real estate property tax deduction, after all.
The IRS will only know what your lender(s) have sent to the government via the Form 1098. But you will have, presumably, your own payment records in the guise of bank statements and / or a printout of your account from the county assessor's office (which you can get in many jurisdictions directly over the internet). That will constitute your "proof" if you are ever asked to justify your property taxes paid deduction.
By way of comparison, for those property owners who receive property tax bills directly from the county (and who don't have or pay their property taxes through their lender), these folks never have their property taxes reported to the IRS via Form 1098 at all . . . so in many instances the IRS has no information on property taxes paid.
Our tax code in the United States functions mostly on the honor system, but with compliance checks. One of those compliance checks is in the form of occasional taxpayer audits. Tax penalties for noncompliance can be harsh. However, if you keep good records, and claim accurate income + deductions, then you have absolutely nothing to worry about.
To return to your original question, you should go with the yearly total of your actual property tax payments, as long as you can prove them, even if this differs from the amounts shown on your Form 1098(s).
