Well, it is also one of my fav songs, so it will be hard to have me accept any other singing than Peter's I guess.
Not sure what type of equipment you have and what you can use for mixing and so on, but if you could tune out the original singing and raise the level of the music so you are more in tune with the singing and the music it would be easier for me to really judge it.
Now it gets too much (for me) focus on your singing, while you still hear Peter in the back, and not enough focus on how your singing goes with the music.
Can't really judge it more/better than that myself I think, other than that I prefer Peter singing this song.
Keep it up though, it's a hell of a lot better than I would be able to perform.