It depends. However, for your situation, both are allowed to tax your income. New York taxes you as a nonresident, and PA taxes you as a resident. When this is the case, your resident state (PA) will give you a credit for the tax you must pay to NY on your income. NY does have a higher tax rate than PA, so it is likely you do not pay PA tax at the time you file your return.
However, you do not want to start having PA tax withheld instead of NY tax. NY gets priority as far as who receives the tax first as long as you work there. Your employer will be required to withhold and remit (send) your taxes to NY on that income unless you are a military spouse only present in NY because of your spouse's marching orders. Otherwise, you are required to pay NY taxes. If these are not withheld, you will owe a substantial amount and will likely face penalties and interest payments for not having paid in enough New York tax. (Yes, you'd get a larger PA refund, but you'd end up losing in the exchange).
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