Why would one choose to pray to an Angel or a Guardian Angel over
Jesus at times?
That is a very good question. I am borrowing here from an answer I had given to a person when I was asked the same question about praying to the saints in heaven.
I think the answer to this question is found in the Fatherly heart of God. God, as a father, desires to glorify his sons and daughters. The way he does that is by using his sons and daughters as instruments of his healing, his forgiveness, his blessings. God, sitting in heaven could have chosen to appear in private to every single person and proclaim the gospel to him individually, but he did not. He chose his sons and daughters to do that job, so that he may glorify them through the mighty works he does through them. This is the mystery behind asking anyone either on earth or in heaven to pray for us. We already pray to Jesus, but sometimes it may be the will of Jesus (and the Father) to grant us a blessing when one of his sons or daughters (other than Jesus) pleads to him on our behalf (note that the angels are considered to be sons of God (Job 1:6)).
We already see this in the scripture itself. In James chapter 5:13-15, we read, "is any one among you suffering?
1. Let HIM PRAY.
2. Let HIM call for the ELDERS of the Church, and let THEM pray over him with oil in the name of the Lord; and the prayer of faith will save the sick man...."
This is quite interesting. The sick man could perhaps have asked, "I already prayed to Jesus. Why should I call the elders of the church to pray for me?" But this example demonstrates to us that it is God's WILL that we seek the help of others in the body of Christ, so that he may have an opportunity to glorify his sons and daughters who then become instruments of his healing.
Thus, it may be that sometimes God wants to answer a particular prayer when we ask an angel to intercede for us. In this way, God glorifies the angel, his son. It is not the case that the angels are more accessible to us than Jesus. Hope this helps.