We can also do both kinds of prayers, if we choose. We are not limited to an either/or, but we can pray directly to God, and we can ask others to pray for us as well. God's written word instructs us to pray for each other, and even though God knows exactly what we need before we ask, He still wants us to pray to Him anyway, as He has clearly revealed in His written word:
If the prayer of a righteous man has great power in its effects, imagine the power the prayer of a holy angel has in its effects.------------------------------------------------------------
...pray for one another, that you may be healed. The prayer of a righteous man has great power in its effects.
James 5:16b------------------------------------------------------------
(I'm not sure why some people have trouble accepting go-betweens for intercessory prayers for others. Though He obviously does not need to, God often chooses to use created go-betweens to do His Holy Will, as He did when He chose all human beings as go-betweens to write every single word in every single "book" in the Bible, and He often chose to use angels as go-betweens, to deliver messages, for example, like you mentioned.)
Very well-said!