Sorry. I got them backwards. Trying to remember Greek isn't always easy :)
Petra- ) a rock, cliff or ledge
a) a projecting rock, crag, rocky ground
b) a rock, a large stone
c) metaph. a man like a rock, by reason of his firmness and strength of soul
Petros- "a rock or a stone
If Jesus were referring to Peter as the rock on which he would build His church, why not say "You are Peter, and YOU are the one I will build my church upon?" He was speaking directly to Peter. Grammatically, it doesn't make sense to say that the two are the same. Now, if Jesus is making a play on words, which I certainly believe that He was, then He was congratulating Peter on his acknowledgement of the truth and saying - that Jesus is the Christ, the Son of the Living God - He will build His church.
The clue is the renaming, as well as the other distinctions given Peter alone: the keys, the charge to feed the sheep, and the promise to pray so that Peter converts his brethren. This means that Jesus meant his Church to be the effort of Peter in some personal and unique way. Your interpretation: "This is a big rock, and you are a small rock" does not fit the broader context.