There's a little story in the book of Matthew where a few disciples have a chance to be with God the Father and Jesus the Son at the same time. They're standing on a mountain when this happens and the commentary reads like this:
"After six days Jesus took with him Peter, James and John, and led them up a high
mountain by themselves. There he was transfigured before them. His face shone like the
sun, and his clothes became as white as the light. Just then there appeared before them
Moses and Elijah, talking with Jesus...While Peter was still speaking a bright cloud
enveloped them, and a voice from the cloud said, 'This is my Son, whom I love; with him
I am well pleased. Listen to him! When the disciples heard this, they fell face down to
the ground, terrified. But Jesus came and touched them. 'Get up', he said. 'Do not be
afraid.' When they got up they saw no one except Jesus." Matthew 17:1-8
The reaction of the disciples to the voice and presence of God is reminiscent of the reaction of the Israelites in the Old Testament when they encountered the awesome presence of God. When I think back to God's revelation of Himself in the Old Testament it seems scary. There is an awesomeness to it. There is a sense of otherness. In God's effort to communicate with humanity he kind of freaks them out. I would suggest this doesn't have so much to do with God being frightening in the sense where the God of the Old Testament is the big finger in the sky pointing at us when we do wrong. Instead I would suggest God is desiring to reveal himself to us, but that revelation is too awesome for us to bear. The glory of God (which literally fills all the earth) is revealed at different times and places in scripture and people can't handle it. In God's attempt to be with Israel there is still a separation.
Enter Jesus.
The disciples standing on the mountaintop are freaked out. They fall to the ground...faces hitting the dirt...and then Jesus approaches them and tells them not to be afraid. Jesus is the divine connection with humanity that makes connection with God the Father possible and perhaps we could say more comfortable. When Jesus is saying 'When you see me, you see the Father' he's telling us that the God who reveals himself is such awesome ways has become one of us...to empathize with us...to learn and live our lives and what they're like. Jesus still possesses the awesome qualities of God, but he is a living, breathing person who translates that awesome character in a way we can understand and relate to. Jesus doesn't replace the awesome nature of the Father, but the Father sends Jesus to us as a further effort to be personable with humanity and to restore the intimacy lost at the Fall.
An off the cuff thought, but what does that say for the oft quoted verse on salvation that Jesus gives when He says 'no one can come to the Father but by me.' Could this be as much a reference to God the Father's continuing revelation of Himself? You can't know the true nature of the Father unless you first know me...because Jesus is God revealing His nature, character, heart, etc in a way we can understand and relate to.