Suppose I'm backing up some Audio CD, which is the better method below?

1) Extract the original Audio CD as an image on hard disk, then burn to CDR;

2) Extract all the tracks in WAV format with EAC to hard disk, then burn the tracks with Nero or other authoring software;

Which of the methods will produce a more perfect copy with better quality?

The quality will be the same (if the CD is in good condition).
But with EAC you'll be sure that extraction has been perfect.
(Also you can specify exact offsets in EAC).

Use "Compare WAVs" tool in EAC to compare WAVs extracted with different methods.

you'd rather both extract an image of the CD and then burn it with a Feurio!® trial version

Both the same. What is important is not to make the copy on the fly. EAC or Feurio are great but nero should be enough most of the times(surely if source cd is in good condition).

I've done this test several times. NEVER use the 'disc image' method. It sounds AWFUL! I alway rip to .wav, then burn.

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The disc image is a WAV file isn't it?

Arkham had remarked that the extraction is the same in a previous post..

What's the misunderstanding here?

The CD Image is one large .wav file with TOC.

@joelmon,

yes, it is .

What I mean image is like ISO or other files by CloneCD or so.

And what I mean is that Feurio! is the best audio CD recording program.
So, my proposal is similar to your point 1),

the only differences are that I suggested you to extract it as a single audio file ( .wav, not ISO-alike ),
( not "all the tracks in WAV format " , although it makes no difference whether they are few of just a big one)
and burn it using the same software, i.e. Feurio ( not EAC ).
And one more thing, the EAC image is also a large .wav file.

Well, I guess it's up to you how you are gonna meet you demands.

best to do it slow if you go for the all at once method. most ears cant tell the difference between teh two methods, though. try it.

You try both methods using the same media/drive combo. You slap the resulting CD in the best hi-fi you can lay your hands on. The best method is the one that sounds best, (for that particular recording/music type).

if you cannot tell the difference, then use the quickest/most convenient method.

If you can tell the difference, provide some ABX blind test results, you'll be the first one in the world (no joking).