My personal view is that in the Scriputes every single word has bee meaningfully chosen for our instruction.
As for agapao and phileo, they are very important words and I believe we can learn a lot from their use also about the relationship between the two concepts they refer to.
I am taking the following considerations from an article I wrote some months ago on my blog dvareloheynu.com (which I am not quoting properly also because it is still only in Italian) about brotherly love (philadelphia in Greek, amicizia fraterna in Italian). My point there is that philia and agàpe are not two different levels of love (in the Gospel of John the love of the Father for the Son is expressed both with agapao - 3:35 - and with philéo - 5:20), but rather two different aspects of the action of being one.
As between looking and seeing, or between forming and creating, between agàpe (love) and philìa (friendship) there is a difference in "aspect", or point of view. Philia's friendship derives from a feeling of affinity, from a certain degree of identity that is perceived with the friend, and it is therefore always reciprocal. Agàpe love, on the other hand, is the act of bridging a distance, producing an identity that was not there yet, or that could not be seen. That is, the difference lies in a different function compared to the identity that is the essence of love: whereas agàpe creates it, philìa assumes it. In fact you can't befriend somebody that you don't know, but somebody that you love even though you don't know him can easily become your friend.
The passage from the last chapter of John's Gospel we are considering here compares these two words closely. Let us read it again with the two verbs used in the original text in brackets for clarity sake: "When they had breakfast, Jesus said to Simon Peter: Simon of Jonah, do you love me (the verb used here is agapào) more than these? He answered: Yes, Lord, you know that I am your friend (philéo). Jesus said to him, "Feed my lambs. He said to him again, a second time: Simon of Jonah, do you love me (agapào)? He said: Yes, Lord; you know that I am your friend (philéo). Jesus said to him, "Pasture my sheep. He said to him the third time: Simon of Jonah, are you my friend (philéo)? Peter was saddened that he had said to him the third time: "Are you my friend (philéo)? And he said to him, Lord, you know everything; you know that I am your friend (philéo). Jesus said to him, "Feed my sheep." (John 21:15-17). It is interesting to note that both Jesus and Peter considered friendship a stronger condition, that is, more difficult and more necessary for a collaborative relationship. As if Jesus were saying: "To feed my sheep, your good intention to serve me is not enough. Only if you are my friend and you are their friend and you feel what I feel and therefore you also feel what they feel, you'll be really able to do the most difficult job of feeding my sheep, otherwise you won't. And Peter was saddened that Jesus was not sure of this feeling, precisely because friendship, unlike agàpe love, is basically a reciprocal feeling.