The apostle Paul set a good example of this:
"To that very end indeed we always pray for YOU, that our God may count YOU worthy of [his] calling and perform completely all he pleases of goodness and the work of faith with power." - 2 Thess. 1:11
But the question is: "Would God listen to the prayer of someone else on a person's behalf more, or would it be the same as if the person prayed for themselves?"
Psalm 65:2 tells us that Jehovah is the "Hearer of prayer" and from the Scriptures above, we can be sure that he listens when prayers of those wholeheartedly devoted to Him pray for one another. Jehovah hears "the prayer of the righteous ones." - Proverbs 15:29. (See: The Bible's Viewpoint - Prayers That Are Heard by God)
So there are some questions that need to be asked about the person praying on behalf of another:
For more, see:
Prayer - Links to Information (Search For Bible Truths)