It depends.  Reporting and programming requirements for NJ/NY require both lines on the W-2, and this double-reporting gets combined in TurboTax (screenshot below will explain how to remove the double-reported income).  However, you do not alter the numbers.  You are going to pay tax in NJ on the NJ taxable income, which may very well be higher than the NY income, because NJ does not allow a deduction for a few items that are deductions in NY and on the Federal return (such as Cafeteria 125 salary reduction plans).  This website provides additional information:NJ Division of Taxation - NJ Income Tax Wages

As you recognize, both NY and NJ tax the income you earn in NY.  However, you will receive a credit on your NJ return for the tax that you pay to NY on the double-taxed income, the income taxed by both states.  But you do not pay tax on double-reported income, as this doubles-up the amount of salary you actually returned.  To remove the double-reported income, please note the following screenshot from the NJ resident return: