Praying out loud brings a difference in answered prayer, for me.
Do I believe it's different because God hears me more? No.
Do I believe I need to say it out loud or louder for God to pay attention? No.
Do I believe God only hears prayers that are said out loud? No.
The difference, at least for me, is that when I hear it out loud, it does something for me.
There is a different level of faith-building intensity when something is just in my mind, versus speaking it out loud.
I have thoughts in my mind that things need to come, or go, but when I speak it and say with confidence and authority and say, "you need to leave" -- wow. I'm amazed by how different it feels. And that feeling tends to fuel a passion to engage in even more prayer, which always brings a difference.