Well isn't you claiming the English is a draw the same as ponz claiming it's as good as e4 and d4? We have no way of really knowing. And that's a good thing.
Is C4 a good opening

"Everything right" is rather relative: 5.e3 was far more ambitious than the meek 5.d3.
Anyway, your only active plan seems to be 8.Bg5 followed at some time by Nc3-e4, but I wouldn't expect more than a very tiny advantage, since white's play up to now has been too nonchallenging, and Black has a sound and solid position.
Despite my reservations I have tried c4 in a recent online game.
I did everything right: played g3 on the second move, did not let my c3 knight to be harrased etc.
This is the position reached after the opening:
Black seems to be rock solid.
C4 experts please help: what is my plan here?
Not surprisingly I agree with pfren. d3 was not a good move choice there and that was the problem. Playing the line badly and then using that as a reason the opening is not good is not a great argument.
My first thought as I clicked through your game was to actually play 4 e3 instead of Nc3. I would have liked that position more, in fact I think I've played that exact sequence once or twice on chess.com.

Playing 4.e2-e3 before Nc3 asks for 4...d5! when suddenly white must start thinking about equality.
4.Nc3 c6 5.e3 is to my taste much preferrable, when neither 5...d5 or 5...d6 look like typical equalizers.
Playing 4.e2-e3 before Nc3 asks for 4...d5! when suddenly white must start thinking about equality.
4.Nc3 c6 5.e3 is to my taste much preferrable, when neither 5...d5 or 5...d6 look like typical equalizers.
Interestingly enough on this site's database (which is a smaller one) there is no game for playing d5 after e3 in that spot. If d5 was that strong of a move you'd expect there to be people playing it there. Without really analyizing the position, I think I'd simply play cxd5 followed by Nc3, if he retreats the knight to b6 the position doesn't look so bad for white and looks similar to when black starts off playing a reversed dragon. Maybe deep analysis would show this to be a bad approach though.
I black instead of 4. ... c6 simply castles (which was the case in my game) 5. e3 does not look that good.
Why do you think it doesn't look good?
It is the main response to that position for a reason. It brings in attacking ideas with a future possible d4. It allows Nge2 to further promote the possible d4 while not blocking the bishop and allowing castling.

5.ed5 Nxd5 6.Nc3?! Nb4 and I can already smell a wandering king (unless you play something like 7.Be4 and swap your light-squared bishop for a knight at no positional gain at all).
6.a3 must be better, but in this strange reversed Kan Sicilian the bishop is very well placed on c5.
@ baatti: The e3/Nge2 idea is perfectly playable after 4...0-0. It's supposed to be suspect using the move sequence 4...Nc6 5.e3 d5 6.cd5 Nb4, but fairly recently Chucky uncorked 7.Nf3!? against Svidler, which to my surprise looks like a good move- neither me, or my friend mr. Houdini were able to find something totally convincing for Black- factly, nothing more than vague "compensation for the pawn".
5.ed5 Nxd5 6.Nc3?! Nb4 and I can already smell a wandering king (unless you play something like 7.Be4 and swap your light-squared bishop for a knight at no positional gain at all).
6.a3 must be better, but in this strange reversed Kan Sicilian the bishop is very well placed on c5.
Fair enough, good points. Maybe I'll spend some time looking at 4. e3 d5 and see what a good response is, it seems like it shouldn't be a problem for white.

4. nf3
black is solid, yes. but the dark squared bishop will be asked some questions in the middlegame that it might not want to answer...
1.c4 e5 2.g3 Nf6 3.Bg2 Bc5 4.Nf3?! e4 when you have to enter 5.Ng5 (5.Ng1 is just too weird) Bxf2+ 6.Kxf2 Ng4+ 7.Kg1 Qxg5 8.Bxe4 Qc5+ 9.d4 Qxc4, when white has to prove that he has enough for his pawn. He probably has, but clearly enough this isn't the way to play for an advantage.
If you are interested in finding out about the English Opening, I found a short 8 minute video that covers the basics. You can find the video at:
http://www.youtube.com/watch?v=L177r53VsPA
There are other videos on youtube as well so you might wish to do a search and see what other videos might be available on this opening.
I only watched the first bit of that but he is showing a fairly obscure english there.
Here's one for you http://chessopenings.com/english+opening/