Palestine would have more right to insist Israel withdraw. And could potentially file charges against Israel at the International Criminal Court. However, on the ground, nothing would change, All parties know this. What the upgrade in status does for the Palestinians is make their negotiating position stronger. This is what the Palestinians are after, since in their eyes, the power disparity with Israel is the main reason negotiations have failed for 20 years. They believe Israel has no incentive to negotiate in good faith (as they can continue to expropriate land unchallenged) and the U.S. has proven it is not able to pressure Israel to level the playing field.
Israeli PM to Palestinian President Abbas: We must fight terror together (Haaretz)
from the article: Palestinians: UN recognition would foster peace with Israel