Years ago, someone gave me a list of Scriptures to pray for your children that Mom's In Touch published. I lost that list a while back, but the concept has stuck with me ever since.
The Word tells us that God's Word does not return void, but will accomplish all that it is sent forth to do.
"So shall My word be that goes forth from My mouth; It shall not return to Me void, But it shall accomplish what I please, And it shall prosper in the thing for which I sent it." Isaiah 55:11
I believe that when we pray Scripture, it's more effective because God's Word is simply more effective than our own.
I have found this to be true in experience. Last year, my five-year-old had a terrible habit of whining and being basically sullen most of the time. I began praying joy and peace Scriptures for her. I typed them up on little cards that I put in my car and in my Bible. Whenever I picked up my Bible, I would pray for her joy. When I was sitting in traffic, I would pray the Scriptures for her. Within a week or so, she was back to her joyful sweet self.
Lately, I have begun praying wisdom and understanding Scriptures for my boys concerning their schoolwork.
God's Word is so powerful. I remember hearing someone say once that when I pray God's Word, it may sound like little 'ol me to my ears, but in the spiritual realm, it sounds like God.