Everyone is commissioned to do that, though. Jesus is specifically, personally commissioning Peter to do something that not everyone is personally commissioned to do.
He is an example to us.We can relate to him as he was a flawed and weak individual. Even seeing Christ transformed at the Transfiguration, he proposed building 3 shrines, one to Christ, and one to Elijah and one to Moses. Paul says that he, Paul, is the least of the apostles, and he himself had to correct Peter on occasion, after the Lord was gone. So, no, he wasn't given anything more than the rest were.
The very fact that the apostles had an argument among themselves shows they did not understand that Peter was to be prince. Also, the occasion of the argument was the night of the betrayal--the last night of the Lord's earthly ministry--and yet the apostles still did not understand that Christ had given Peter a position of primacy. The Lord settled the argument, not by stating that He had already made Peter head, but by declaring that the Gentiles have their heads, "But not so with you." Thus, Jesus very plainly taught that no one would occupy any such place as a Benefactor (or Pope) to exercise authority over the others.