In the Gospel of John (John 1:43-51, Nathanael claimed "thou art the Son of God; thou art the King of Israel." When Peter proclaimed "Thou art the Christ, the Son of the living God," (Matthew 16:16). Why did Jesus praise Peter for saying without being shown?
IIt appears that Nathanael Bartholomew was the first of the Apostles to acknowledge the deity and Messiahship of Jesus. Nathanael realized that Jesus was the Messiah and the Son of God through the miracle of Jesus seeing him under a fig tree. Peter's response is only slightly different. There had been many miracles by Jesus up to this point, but the group has been silent on who Jesus really was, other than a Rabbi.
It was only Peter and not Nathanael that responded to Jesus' question"But whom say ye that I am?" (Mt 16:15)
I would recommend that the answer centers on the role of Peter within the group. So in front of the disciples, Jesus separates Peter's response as he will become the leader of the Apostles. This is like an acknowledgement from Jesus, that what Peter says has merit and weight.
Doing a little more reading last night, jesus praised Peter because "flesh and blood did not reveal this to you". Philip told Nathanuel "we have found the messiah". Could that be what Jesus was referring to with the way he affirmed Peter?
Daniel, I believe that is the main piece in understanding Christ's response to Peter as compared to Nathanael. There are many facets to trying to understand why there was a difference in His response.
One other thing (by the way, great question), the audience was different. In the Gospel of John, it appears that this was a "private" audience between Jesus and Nathanael, whereas, the incident with Peter was in the audience with the other disciples. Jesus asked the question of all the disciples and Peter responds.
I believe Nathanael as a Jewish man was open to the coming of the Messiah and acknowledged the fulfillment of the scripture prophecy in Jesus as Rabbi, Son of God and King of Israel. Peter responded not because of knowledge he had learned but by the revelation of God's work in his spiritual heart.